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1
Murphy, Thomas E., Adam B. Cohen, Bhargava Ravoori, Karl R. B. Schmitt, Anurag V. Setty, Francesco Sorrentino, Caitlin R. S. Williams, Edward Ott, and Rajarshi Roy. "Complex dynamics and synchronization of delayed-feedback nonlinear oscillators." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1911 (January 28, 2010): 343–66. http://dx.doi.org/10.1098/rsta.2009.0225.
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We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.
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Li, XiaoFu, Md Raf E Ul Shougat, Tushar Mollik, Robert N. Dean, Aubrey N. Beal, and Edmon Perkins. "Field-programmable analog array (FPAA) based four-state adaptive oscillator for analog frequency analysis." Review of Scientific Instruments 94, no. 3 (March 1, 2023): 035103. http://dx.doi.org/10.1063/5.0129365.
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Adaptive oscillators are a subset of nonlinear oscillators that can learn and encode information in dynamic states. By appending additional states onto a classical Hopf oscillator, a four-state adaptive oscillator is created that can learn both the frequency and amplitude of an external forcing frequency. Analog circuit implementations of nonlinear differential systems are usually achieved by using operational amplifier-based integrator networks, in which redesign procedures of the system topology is time consuming. Here, an analog implementation of a four-state adaptive oscillator is presented for the first time as a field-programmable analog array (FPAA) circuit. The FPAA diagram is described, and the hardware performance is presented. This simple FPAA-based oscillator can be used as an analog frequency analyzer, as its frequency state will evolve to match the external forcing frequency. Notably, this is done without any analog-to-digital conversion or pre-processing, making it an ideal frequency analyzer for low-power and low-memory applications.
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Kitio, Gabin Jeatsa, Cyrille Ainamon, Karthikeyan Rajagopal, Léandre Kamdjeu Kengne, Sifeu Takougang Kingni, and Justin Roger Mboupda Pone. "Four-Scroll Hyperchaotic Attractor in a Five-Dimensional Memristive Wien Bridge Oscillator: Analysis and Digital Electronic Implementation." Mathematical Problems in Engineering 2021 (October 19, 2021): 1–21. http://dx.doi.org/10.1155/2021/4820771.
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An electronic implementation of a novel Wien bridge oscillation with antiparallel diodes is proposed in this paper. As a result, we show by using classical nonlinear dynamic tools like bifurcation diagrams, Lyapunov exponent plots, phase portraits, power density spectra graphs, time series, and basin of attraction that the oscillator transition to chaos is operated by intermittency and interior crisis. Some interesting behaviors are found, namely, multistability, hyperchaos, transient chaos, and bursting oscillations. In comparison with some memristor-based oscillators, the plethora of dynamics found in this circuit with current-voltage (i–v) characteristic of diodes mounted in the antiparallel direction represents a major advance in the knowledge of the behavior of this circuit. A suitable microcontroller based design is built to support the numerical findings as these experimental results are in good agreement.
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Spanos, P. D., A. Sofi, and M. Di Paola. "Nonstationary Response Envelope Probability Densities of Nonlinear Oscillators." Journal of Applied Mechanics 74, no. 2 (February 6, 2006): 315–24. http://dx.doi.org/10.1115/1.2198253.
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The nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic averaging, the procedure relies on the Markovian modeling of the response envelope process through the definition of an equivalent linear system with response-dependent parameters. An approximate solution of the associated Fokker-Planck equation is derived by resorting to a Galerkin scheme. Specifically, the nonstationary probability density function of the response envelope is expressed as the sum of a time-dependent Rayleigh distribution and of a series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. These functions are the eigenfunctions of the boundary-value problem associated with the Fokker-Planck equation governing the evolution of the probability density function of the response envelope of a linear oscillator. The selected basis functions possess some notable properties that yield substantial computational advantages. Applications to the Van der Pol and Duffing oscillators are presented. Appropriate comparisons to the data obtained by digital simulation show that the method, being nonperturbative in nature, yields reliable results even for large values of the nonlinearity parameter.
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VIEIRA, MARIA DE SOUSA, ALLAN J. LICHTENBERG, and MICHAEL A. LIEBERMAN. "NONLINEAR DYNAMICS OF DIGITAL PHASE-LOCKED LOOPS WITH DELAY." International Journal of Bifurcation and Chaos 04, no. 03 (June 1994): 715–26. http://dx.doi.org/10.1142/s0218127494000514.
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We investigate numerically and analytically the nonlinear dynamics of a system consisting of two self-synchronizing pulse-coupled nonlinear oscillators with delay. The particular system considered consists of connected digital phase-locked loops. We find mapping equations that govern the system and determine the synchronization properties. We study the bifurcation diagrams, which show regions of periodic, quasiperiodic and chaotic behavior, with unusual bifurcation diagrams, depending on the delay. We show that depending on the parameter that is varied, the delay will have a synchronizing or desynchronizing effect on the locked state. The stability of the system is studied by determining the Liapunov exponents, indicating marked differences compared to coupled systems without delay.
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Shabunin, Aleksej. "Selection of spatial modes in an ensemble of non-locally coupled chaotic maps." Izvestiya VUZ. Applied Nonlinear Dynamics 30, no. 1 (January 31, 2022): 109–24. http://dx.doi.org/10.18500/0869-6632-2022-30-1-109-124.
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Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters. Correlation between the spatial spectra and the amplitude-frequency response of the coupling filter and the mutual coherence of oscillations when the coupling parameters change were considered. Results. The system of couplings between chaotic maps behaves like a wave filter with selective properties, allowing spatial modes with certain wavelengths to exist and suppressing others. The selection of spatial modes is based on the wave characteristic of the coupling filter, the type of which is determined by the radius and the magnitude of couplings. At strong coupling the wave characteristics for ensembles with local and non-local couplings are qualitatively different, therefore they demonstrate essencially different behavior. Discussion. Using spectral methods for dynamics analysis systems with complex network topologies seems to be a promising approach, especially for research of synchronization and multistability in ensembles of chaotic oscillators and maps. The found regularities generalize the results known for ensembles of maps with local couplings. They also can be applied to ensembles of self-sustained oscillators.
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Krenk, S., and J. B. Roberts. "Local Similarity in Nonlinear Random Vibration." Journal of Applied Mechanics 66, no. 1 (March 1, 1999): 225–35. http://dx.doi.org/10.1115/1.2789151.
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A response analysis procedure is developed for oscillators with highly nonlinear stiffness and light nonlinear damping excited by non-white wide-band random noise based on local similarity between the random response and the deterministic response at the same energy level of the corresponding undamped oscillator. The analysis consists of three parts: introduction of modified phase plane variables, derivation of an approximate general form of the probability density of the response energy. for non-white excitation, and derivation of the spectral density function of the response from the conditional covariance function for a given energy level. The use of modified phase plane variables leads to a completely symmetric formulation and reformulates the stiffness nonlinearity as a nonlinear variation of the instantaneous angular frequency, and thereby a local rescaling of time. The probability density is obtained by averaging the full Fokker-Plank-Kolmogorov equation using local similarity, thus avoiding some theoretical problems associated with the traditional averaging of the stochastic differential equations. The use of local similarity with the exact undamped solution in the derivation of the conditional spectral density leads to a spectral density estimate, that contains the higher harmonic components explicitly. Comparisons of theoretical predictions with digital simulation estimates of both the probability and spectral densities for the Duffing oscillator demonstrate the accuracy of the theory.
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Roy, R. V. "Noise-Induced Transitions in Weakly Nonlinear Oscillators Near Resonance." Journal of Applied Mechanics 62, no. 2 (June 1, 1995): 496–504. http://dx.doi.org/10.1115/1.2895957.
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We investigate the noise-induced transitions between the oscillatory steady states of a class of weakly nonlinear oscillators excited by resonant harmonic forcing. We begin by deriving a set of averaged equations governing slow variables of the system when the latter is perturbed by both additive white Gaussian noise and by random phase fluctuations of the resonant excitation. We then examine in detail the behavior of the reduced system in the case of cubic stiffness and viscous damping forces. Three regimes are examined: the case of weak damping, the case of near-bifurcation and the more general case when neither of the first two situations apply. In each case we predict the quasi-stationary probability density of the response and the mean time taken by the trajectories to pass from one basin of attraction to the other. These theoretical predictions are based on averaging of a near-Hamiltonian system in the weak damping limit, on center-manifold theory in the near-bifurcation case, or on Wentzell-Kramers-Brillouin (WKB) singular perturbation expansions in the more general case. These predictions are compared with digital simulations which show excellent agreement. We can then determine the probability of a transition for each state and for all parameter values. For this, we compute contour curves of the activation energy of each attractor in the parameter plane to yield a complete picture of the survivability of the system subject to random perturbations.
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Roy, R. Vale´ry, and P. D. Spanos. "Power Spectral Density of Nonlinear System Response: The Recursion Method." Journal of Applied Mechanics 60, no. 2 (June 1, 1993): 358–65. http://dx.doi.org/10.1115/1.2900801.
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Spectral densities of the response of nonlinear systems to white noise excitation are considered. By using a formal solution of the associated Fokker-Planck-Kolmogorov equation, response spectral densities are represented by formal power series expansion for large frequencies. The coefficients of the series, known as the spectral moments, are determined in terms of first-order response statistics. Alternatively, a J-fraction representation of spectral densities can be achieved by using a generalization of the Lanczos algorithm for matrix tridiagonalization, known as the “recursion method.” Sequences of rational approximations of increasing order are obtained. They are used for numerical calculations regarding the single-well and double-well Duffing oscillators, and Van der Pol type oscillators. Digital simulations demonstrate that the proposed approach can be quite reliable over large variations of the system parameters. Further, it is quite versatile as it can be used for the determination of the spectrum of the response of a broad class of randomly excited nonlinear oscillators, with the sole prerequisite being the availability, in exact or approximate form, of the stationary probability density of the response.
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Dovbnya, Vitaly G., and Dmitry S. Koptev. "MATHEMATICAL MODEL OF THE RECEIVING PATH OF DIGITAL COMMUNICATION LINES." T-Comm 15, no. 5 (2021): 52–57. http://dx.doi.org/10.36724/2072-8735-2021-15-5-52-57.
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Modern trends in the development of digital communication lines of fixed information transmission services, as well as the characteristics of continuous channels today determine the noise immunity of radio receiving systems. The main directions of its increase in terms of the radio receiving device as a whole and the demodulator device in particular are as follows: reducing the frequency and nonlinear distortions of the signal in the linear path, increasing the stability and purity of the spectral line of oscillations of local oscillators, increasing the selectivity for the mirror and combination channels of reception, compensation for intersymbol and cross – polarization interference, improving the functioning of the automatic gain control device (reducing static and dynamic errors), improving the quality of the functioning of the carrier wave recovery device and the clock synchronization device. Taking into account all of the above factors in order to increase the overall noise immunity of a digital communication line is a very difficult and urgent task, the solution of which must begin with the development of a mathematical model of a continuous digital communication line channel. This article discusses the radio receiving path of a digital communication line in an urban environment. The obtained analytical expressions are aimed at interpreting the processes of converting digital signals in the structural elements of radio receiving systems. The originality of the mathematical model developed in the article lies in the fact that it additionally, in comparison with similar models, takes into account the following number of factors: frequency instability and phase fluctuations of oscillations of the local oscillator synthesizer, dynamic and static errors in the operation of automatic gain control devices, carrier vibration recovery devices and devices clock synchronization of radio receiving systems of digital signals.
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Tamaševičiūtė, Elena, and Gytis Mykolaitis. "Analogue modelling an array of the FitzHugh–Nagumo oscillators." Nonlinear Analysis: Modelling and Control 17, no. 1 (January 25, 2012): 118–25. http://dx.doi.org/10.15388/na.17.1.14082.
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The purpose of the paper is to show that analogue electronic modelling is an extremely fast technique compared to conventional digital computing, especially when solving large sets of coupled nonlinear differential equations. An array of thirty FitzHugh–Nagumo type electronic oscillators, modelling dynamics of the brain neurons, is considered. The decrease of time consumption by a factor of several thousands is demonstrated. The work delivers a perspective of how to implement convenient analogue models of complex dynamical networks.
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Wonchoba, W. E., M. A. Lieberman, and A. J. Lichtenberg. "The dynamics of a class of coupled digital oscillators." Nonlinearity 7, no. 6 (November 1, 1994): 1695–715. http://dx.doi.org/10.1088/0951-7715/7/6/009.
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Carley, D. W., E. Onal, R. Aronson, and M. Lopata. "Breath-by-breath interactions between inspiratory and expiratory duration in occlusive sleep apnea." Journal of Applied Physiology 66, no. 5 (May 1, 1989): 2312–19. http://dx.doi.org/10.1152/jappl.1989.66.5.2312.
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We examined interactions between inspiratory duration (TI), expiratory duration (TE), and inspiratory (esophageal) pressure (Pes) generation in seven subjects with confirmed occlusive sleep apnea. Breath-by-breath values of TI, TE, and Pes were identified by digital computer during 21 260-s epochs of repetitive occlusive apnea during non-rapid-eye-movement sleep. The control theory of interacting nonlinear oscillators was used to categorize the interaction between TI and TE for each epoch as either 1) synchronization, the strongest possible interaction between biological oscillators; 2) relative entrainment, a moderate interaction between oscillators; or 3) relative coordination, a weak interaction. The latter two interactions were characterized by systemic oscillations in the moving cross-correlation between TI and TE. The relationship between TI and Pes was analyzed in a similar fashion. Significant oscillations were present in all three parameters (P less than 0.0001 for each). We observed significant negative correlations between TI and TE and between TI and Pes (P less than 0.001 for each) when all breaths for all epochs were pooled. In no epoch was there a significant positive correlation between TI and TE or Pes. All three interactions were observed between TI and TE: five epochs of synchronization, nine of relative entrainment, and seven of relative coordination. In contrast, 19 of 21 epochs exhibited synchronization between TI and Pes, with 2 epochs of relative entrainment. The relative frequency of TI vs. Pes synchronization was significantly greater than TI vs. TE synchronization (P less than 0.005).(ABSTRACT TRUNCATED AT 250 WORDS)
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Hart, Joseph D., Laurent Larger, Thomas E. Murphy, and Rajarshi Roy. "Delayed dynamical systems: networks, chimeras and reservoir computing." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2153 (July 22, 2019): 20180123. http://dx.doi.org/10.1098/rsta.2018.0123.
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We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.
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Proskuryakov, K. N., and A. V. Anikeev. "Self-oscillations that cause the destruction of intermolecular bonds in the water coolant of a nuclear power plant." Journal of Physics: Conference Series 2127, no. 1 (November 1, 2021): 012055. http://dx.doi.org/10.1088/1742-6596/2127/1/012055.
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Abstract The digital acoustic model of a nuclear reactor (DAMNR) is presented as an auto-oscillatory system belonging to a special class of nonlinear dissipative systems capable of generating undamped oscillations. It is established that a water-water power reactor with a turbulent flow of a coolant is an open system of high complexity with a large number of elements, the connections between which are not predetermined, but probabilistic. Elements of the coolant circuit with negative dissipation (negative friction) are identified. It is shown that they self-organize chaotic turbulent pulsations and vortices into ordered wave oscillations, the frequency of which is determined by the Thomson (Kelvin) formula. In radio engineering circuits, an electronic self-oscillating generator with transformer feedback has similar properties. The presence of negative resistance in nonlinear dynamical systems leads to self-organization of chaotic turbulent perturbations and generation of self-oscillations in the form of acoustic standing waves (ASW). On the basis of theoretical and experimental data, the reliability of a previously unknown property of a reactor with connected pipelines - the ability to generate several ASW simultaneously-was confirmed. The use of DAMNR in the design and operation of nuclear power plants allows to identify the sources of ASW occurring in the coolant, the conditions for their occurrence and frequency.
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STAVRINIDES, S. G., A. N. MILIOU, TH LAOPOULOS, and A. N. ANAGNOSTOPOULOS. "THE INTERMITTENCY ROUTE TO CHAOS OF AN ELECTRONIC DIGITAL OSCILLATOR." International Journal of Bifurcation and Chaos 18, no. 05 (May 2008): 1561–66. http://dx.doi.org/10.1142/s0218127408021178.
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An electronic oscillator producing digital signals, formed by a second-order, nonlinear, nonautonomous, closed loop topology that is based on two integrators and nonlinear elements (a comparator and a XOR gate), was experimentally investigated. For a certain frequency and amplitude range of the periodic driving signal, the intermittency route to chaos was observed and studied.
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MOON, F. C., M. A. JOHNSON, and W. T. HOLMES. "CONTROLLING CHAOS IN A TWO-WELL OSCILLATOR." International Journal of Bifurcation and Chaos 06, no. 02 (February 1996): 337–47. http://dx.doi.org/10.1142/s0218127496000084.
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The chaotic dynamics of a nonlinear buckled elastic beam are shown to be controllable in a periodic orbit using a digital occasional proportional feedback control circuit. The method is similar to that developed by Hunt [1991] and does not require a detailed knowledge of the underlying two-dimensional map. The control is effected by perturbing the potential wells synchronously with the forcing function. Experiments show that the system possesses both periodic orbits and strange attractors different than those of the uncontrolled system.
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BARAJAS-RAMÍREZ, JUAN-GONZALO, GUANRONG CHEN, and LEANG S. SHIEH. "HYBRID CHAOS SYNCHRONIZATION." International Journal of Bifurcation and Chaos 13, no. 05 (May 2003): 1197–216. http://dx.doi.org/10.1142/s021812740300714x.
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The problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chaotic systems, Chua's circuit, Duffing oscillator, and Chen's system, are simulated thereby validating the novel design proposed in this paper.
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Pavlenko, Yurii, Sergii Kirienko, Valeriy Ogar, and Olena Vаsileva. "Research of metrological capabilities of digital (DDS- and Trueform-) generators." Ukrainian Metrological Journal, no. 3 (October 5, 2021): 3–9. http://dx.doi.org/10.24027/2306-7039.3.2021.241500.
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Abstract
One of the fundamental improvements of the measurement standard of frequency deviation of frequency-modulated oscillations was the replacement of analog frequency-modulated generators used in DETU 09-03-95 with digital ones based on the principle of direct digital synthesis (DDS) and its next version of Trueform technology. These generators have wider ranges of frequency deviation and modulation frequencies than analog ones, but nonlinear distortion laws of the frequency modulation are not standardized.
The subject of the article is the development of methods and research of these generators and frequency-modulated signals generated by them for nonlinear distortions, accompanying amplitude modulation, frequency noise. Three methods were used in the study: direct measurement; “combination frequencies” and “frequency shift”. The experiment was performed using several measurement methods, which allowed to estimate very small values of nonlinear distortion. Methods were developed and experimental estimations of concomitant amplitude modulation of DDS-generators (in frequency modulation mode), as well as their frequency noise level, were performed. An experimental evaluation of the capabilities of the analog-digital demodulator of the R&S FSL6 spectrum analyzer with the K7 option was performed, its high linearity was shown, its capabilities with respect to the frequency ranges of carrier oscillations and frequency deviation were evaluated. The research results provide a basis for the method of calibration of DDS-generators and demodulator of spectrum analyzers with the K7 option in those ranges where their parameters are not normalized (at direct current up to 8 MHz and F up to 500 kHz).
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Dao, Nguyen Van. "Interaction between the elements characterizing the forced and parametric excitations." Vietnam Journal of Mechanics 20, no. 1 (March 30, 1998): 9–20. http://dx.doi.org/10.15625/0866-7136/10008.
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In nonlinear systems, the first order of smallness terms of nonresonance forced and parametric excitations have no effect on the oscillation in the first an approximation. However, they do interact one with another in the second approximation.Using the asymptotic method of nonlinear mechanics [1] we obtain the equations for the amplitudes and phases of oscillation. The amplitude curves are drawn digital computer. The stationary oscillations and their stability are of special interest.
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Li, Mengyu, Christopher Bernitsas, Guo Jing, and Sun Hai. "Hydrokinetic Power Conversion Using Vortex-Induced Oscillation with Cubic Restoring Force." Energies 13, no. 12 (June 25, 2020): 3283. http://dx.doi.org/10.3390/en13123283.
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A cubic-spring restoring function with high-deformation stiffening is introduced to passively improve the harnessed marine hydrokinetic power by using flow-induced oscillations/vibrations (FIO/V) of a cylinder. In these FIO/V experiments, a smooth, rigid, single-cylinder on elastic end-supports is tested at Reynolds numbers ranging from 24,000 < Re < 120,000. The parameters of the tested current energy converter (CEC) are cubic stiffness and linear damping. Using the second generation of digital virtual spring-damping (Vck) controller developed by the Marine Renewable Energy Laboratory (MRELab), the cubic modeling of the oscillator stiffness is tested. Experimental results show the influence of the parameter variation on the amplitude, frequency, energy conversion, energy efficiency, and power of the converter. All experiments are conducted in the low turbulence-free surface water (LTFSW) channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinearity in the cubic oscillator is an effective way to extend the vortex-induced vibration (VIV) upper branch, which results in higher harnessing power and efficiency compared to the linear stiffness cylinder converter. (2) Compared to the linear converter, the overall power increase is substantial. The nonlinear power optimum, occurring at the end of the VIV upper branch, is 63% higher than its linear counterpart. (3) The cubic stiffness converter with low harnessing damping achieves consistently good performance in all the VIV regions because of the hardening restoring force, especially at higher flow velocity.
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Wang, Guangyi, Shiyi Jiang, Xiaowei Wang, Yiran Shen, and Fang Yuan. "A Novel Memcapacitor Model and Its Application for Generating Chaos." Mathematical Problems in Engineering 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/3173696.
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Memristor and memcapacitor are new nonlinear devices with memory. We present a novel memcapacitor model that has the capability of capturing the behavior of a memcapacitor. Based on this model we also design a chaotic oscillator circuit that contains a HP memristor and the memcapacitor model for generating good pseudorandom sequences. Its dynamic behaviors, including equilibrium points, stability, and bifurcation characteristics, are analyzed in detail. It is found that the proposed oscillator can exhibit some complex phenomena, such as chaos, hyperchaos, coexisting attractors, abrupt chaos, and some novel bifurcations. Moreover, a scheme for digitally realizing this oscillator is provided by using the digital signal processor (DSP) technology. Then the random characteristics of the chaotic binary sequences generated from the oscillator are tested via the test suit of National Institute of Standards and Technology (NIST). The tested randomness definitely reaches the standards of NIST and is better than that of the well-known Lorenz system.
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Kumar, Mani Kant, and Haranath Kar. "Analysis of Memory Effects in Digital Filters with Overflow Arithmetic." Indonesian Journal of Electrical Engineering and Computer Science 7, no. 3 (September 1, 2017): 755. http://dx.doi.org/10.11591/ijeecs.v7.i3.pp755-760.
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<p>This paper deals with the problem of undesired memory effects in nonlinear digital<br />filters owing to the influence of past excitations on future outputs. The nonlinearities under consideration cover the usual types of overflow arithmetic employed in practice. Based on the Hankel norm performance, a new criterion is proposed to ensure the reduction of undesired memory effects in digital filters with overflow arithmetic. In absence of external input, the nonexistence of overflow oscillations is also confirmed by the proposed criterion. A numerical example together with simulation result showing the effectiveness of the criterion is given.</p>
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Karimov, Timur, Denis Butusov, Valery Andreev, Artur Karimov, and Aleksandra Tutueva. "Accurate Synchronization of Digital and Analog Chaotic Systems by Parameters Re-Identification." Electronics 7, no. 7 (July 20, 2018): 123. http://dx.doi.org/10.3390/electronics7070123.
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The verification of the digital models of chaotic systems and processes is a valuable problem in many practical applications, such as nonlinear control and communications. In our study, we propose a hybrid technique for chaotic systems’ identification, based on the chaotic synchronization of digital and analog counterparts and a numerical optimization method used for the fine tuning of parameters. An analog circuit implementing the Rössler oscillator with digitally controlled parameters was chosen as an identification object, and the FPGA model was used as a digital counterpart for coupling and parameter retrieval. The synchronization between analog and digital chaotic models can be used to estimate the quality of an identification procedure. The results of this study clarify the practical bounds of digital and analog systems’ equivalence. They also contribute to the problem of designing technical systems possessing advantages of both analog and digital chaotic generators (e.g., a high accuracy and protection from quasi-chaotic oscillation modes).
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Carlà, Marcello. "The analog computer: Beyond the museum artwork, a tool for studying linear and nonlinear systems." American Journal of Physics 90, no. 4 (April 2022): 263–72. http://dx.doi.org/10.1119/10.0009634.
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Analog computers have been a valuable resource for a time to solve linear as well as nonlinear differential equations before being superseded by digital computers. However, interest toward analog computing has not fully faded away. Though not competitive for accuracy or speed, analog computers have the important property of being true physical systems that can be made to behave according to a given equations set. This aspect makes analog computers interesting educational tools for hands-on work with real physical systems, where a number of effects, both linear and not linear, can easily be added at will (a feature not readily available in mechanical systems). This paper describes the implementation of a modular, very flexible, cheap, yet powerful analog computer, suitable for student laboratories. As examples of possible applications, a selection of linear and nonlinear oscillator models are described that can be used in the laboratory to introduce students to various nonlinear effects.
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Goto, Hayato, Kosuke Tatsumura, and Alexander R. Dixon. "Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems." Science Advances 5, no. 4 (April 2019): eaav2372. http://dx.doi.org/10.1126/sciadv.aav2372.
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Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.
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BERNHARDT, PAUL A. "COMMUNICATIONS USING CHAOTIC FREQUENCY MODULATION." International Journal of Bifurcation and Chaos 04, no. 02 (April 1994): 427–40. http://dx.doi.org/10.1142/s0218127494000289.
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Chaotic Frequency Modulation (CFM) provides the basis for a nonlinear communications system with (1) good noise suppression and (2) analogue signal encryption for private and secure communications links. CFM is a generalization of conventional Wideband Frequency Modulation (WFM) where the information about modulation samples mk are contained in the lengths of the periods pk for the kth cycle of the WFM waveform. A WFM modulator produces waveform periods described by an invertible function of the form pk=F(mk). Chaotic FM uses a map of the pulse periods to produce a noise-like pulse train even with a constant signal. The basis for CFM is a function pk=F(mk; pk−1, pk−2, …, pk−i), where i is the dimensionality of the map. A practical realization for a CFM transmitter employs an autonomous chaotic relaxation oscillator (ACRO) circuit for use as a chaotic voltage-controlled oscillator (CVCO). The ACRO is simple to construct, consisting of only two capacitors, one inductor, a bistable nonlinear element, and a modulated current source. The CVCO period (pk) is a nonlinear function of the current (mk) and the two previous pulse periods. Demodulation requires the use of at least three successive waveform-periods. Experimental and theoretical studies of the CVCO circuit have shown that (1) the ACRO return maps of pulse periods are embedded in three dimensions, (2) chaotic outputs are difficult to decode without prior knowledge of the circuit parameters, and (3) demodulation may be accomplished with a digital signal processor.
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Yang, Wendi, Hanjun Jiang, and Zhihua Wang. "A 0.0014 mm2 150 nW CMOS Temperature Sensor with Nonlinearity Characterization and Calibration for the −60 to +40 °C Measurement Range." Sensors 19, no. 8 (April 13, 2019): 1777. http://dx.doi.org/10.3390/s19081777.
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This work presents a complementary metal–oxide–semiconductor (CMOS) ultra-low power temperature sensor chip for cold chain applications with temperatures down to −60 °C. The sensor chip is composed of a temperature-to-current converter to generate a current proportional to the absolute temperature (PTAT), a current controlled oscillator to convert the current to a frequency signal, and a counter as the frequency-to-digital converter. Unlike the conventional linear error calibration method, the nonlinear error of the PTAT current under the low temperature range is fully characterized based on the device model files provided by the foundry. Simulation has been performed, which clearly shows the nonlinear model is much more accurate than the linear model. A nonlinear error calibration method, which requires only two-point calibration, is then proposed. The temperature sensor chip has been designed and fabricated in a 0.13 μm CMOS process, with a total active die area of 0.0014 mm2. The sensor only draws a 140 nA current from a 1.1 V supply, with the key transistors working in the deep subthreshold region. Measurement results show that the proposed nonlinear calibration can decrease the measurement error from −0.9 to +1.1 °C for the measurement range of −60 to +40 °C, in comparison with the error of −1.8 to +5.3 °C using the conventional linear error calibration.
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Wang, Lixin, Chang Lu, Hailiang Liu, and Ting Yue. "Method of predicting nonlinear pilot-induced oscillations due to flight control degradation based on digital virtual flight." Aerospace Science and Technology 116 (September 2021): 106871. http://dx.doi.org/10.1016/j.ast.2021.106871.
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KIM, G. B., M. NA, G. ACBAS, B. D. MCCOMBE, S. WANG, M. CHEON, H. LUO, X. LIU, Y. SASAKI, and J. K. FURDYNA. "HIGH-FIELD MAGNETOTRANSPORT STUDIES OF FERROMAGNETIC GaAs/Mn DIGITAL ALLOYS." International Journal of Modern Physics B 18, no. 27n29 (November 30, 2004): 3735–43. http://dx.doi.org/10.1142/s0217979204027372.
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Magnetotransport properties of ferromagnetic GaAs / Mn digital alloys have been investigated in fields up to 33 T. A series of four GaAs / Mn digital alloys with different Mn coverages (0.15 ML - 0.5 ML) at fixed GaAs spacer thickness (9 ML), with Curie temperatures, TC, between 20 and 40 K shows hopping conduction behavior in the zero-field sheet resistance below TC. Analysis of the high field magnetotransport measurements on these samples reveals hole densities between 0.45×1013 and 1.8×1013 cm -2/ Mn layer at 5 K. In contrast, a GaAs / Mn digital alloy with slightly different parameters (0.5 ML Mn and 14 ML GaAs spacer layers) and growth conditions shows essentially metallic behavior and much higher TC (60 K). The zero-field sheet resistance, although decreasing weakly with T at low temperatures, cannot be fit by a hopping expression. From analysis of Shubnikov-de Haas oscillations observed in this sample, an effective mass of ≈0.31m0 was determined, close to the heavy hole mass of GaAs . The hole density extracted from fits to RHall at high fields is comparable to that of the insulating GaAs / Ma digital alloys at the same Mn coverage. This suggests that the increased metallicity is the most important factor in significantly enhancing TC.
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Rymarski, Zbigniew, and Krzysztof Bernacki. "Technical Limits of Passivity-Based Control Gains for a Single-Phase Voltage Source Inverter." Energies 14, no. 15 (July 28, 2021): 4560. http://dx.doi.org/10.3390/en14154560.
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Passivity-based control (PBC) seems to be predicted for the control algorithms in the voltage source inverters (VSI) for voltage backup systems. This paper presents limitations of the improved (IPBC) version of the PBC (directly measuring the output voltage) maximum voltage and current gains. In a microprocessor-controlled inverter, these depend on the PWM modulator dynamic properties, the switching frequency, the modulation index value (avoiding modulator saturation and enabling the rapid increase of the filter inductor current), and the parameters of the VSI output filter. A single switching period delay of the digital PWM modulator was considered in the theoretical calculations based on a discrete inverter model. The simulations for the standard nonlinear rectifier RC load enabled the initial adjustment of the IPBC border gains, which depended on the switching frequency. Some small harmonics oscillations of the output voltage were acceptable for the test rectifier RC load or dynamic load. However, oscillations of the inductor current increased the power losses in the coil core. Experimental verification of the simulation results using a laboratory VSI model is also presented.
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Anttila, Lauri, Peter Händel, Olli Mylläri, and Mikko Valkama. "Recursive learning-based joint digital predistorter for power amplifier and I/Q modulator impairments." International Journal of Microwave and Wireless Technologies 2, no. 2 (April 2010): 173–82. http://dx.doi.org/10.1017/s1759078710000280.
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The main implementation impairments degrading the performance of direct-conversion radio transmitters are in-phase/quadrature (I/Q) mismatch, local oscillator (LO) leakage, and power amplifier (PA) nonlinear distortion. In this article, we propose a recursive least-squares-based learning algorithm for joint digital predistortion (PD) of frequency-dependent PA and I/Q modulator impairments. The predistorter is composed of a parallel connection of two parallel Hammerstein (PH) predistorters and an LO leakage compensator, yielding a predistorter which as a whole is fully linear in the parameters. In the parameter estimation stage, proper feedback signal from the transmitter radio frequency (RF) stage back to the digital parts is deployed, combined with the indirect learning architecture and recursive least-squares training. The proposed structure is one of the first techniques to explicitly consider the joint estimation and mitigation of frequency-dependent PA and I/Q modulator impairments. Extensive simulation and measurement analysis is carried out to verify the operation and efficiency of the proposed PD technique. In general, the obtained results demonstrate linearization and I/Q modulator calibration performance clearly exceeding the performance of current state-of-the-art reference techniques.
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Mbitu, Elisabeth Tansiana, and Seng-Chi Chen. "Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods." Mathematics 8, no. 11 (November 6, 2020): 1978. http://dx.doi.org/10.3390/math8111978.
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This paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither parameters and analyze the existence of limit cycles. This method was done in a nonlinear system with relay nonlinearity using three standard dither signals, namely sine, triangle, and square waves. The aim of choosing varying dithers was to investigate the effect of dither shapes and the minimum amplitude required for the quenching strategy. First, the possibility and amplitude of limit cycles were determined graphically on the DIDF curve. Then, the minimum amplitude of dither was calculated based on the DIDF analysis. Finally, a simulation was built to verify the analytical work using a digital computer. The simulation results were related to the analysis results. It was evident that the dithering technique is a simple way to suppress limit cycles in a nonlinear system. This paper also presented that dither is an amplitude function, and square-wave dither has the minimum amplitude to quench limit cycles.
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Chatterjee, Basab, Surjadeep Sarkar, and Falguni Sinhababu. "Modification over Dithered DPLL to reduce the effect of narrowband channel interference." YMER Digital 21, no. 06 (June 14, 2022): 383–91. http://dx.doi.org/10.37896/ymer21.06/37.
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Digital signal processing based digital phase locked loop (DSP DPLL) are most commonly used for carrier phase tracking in the recent times. Phase locked loop (PLL) behaves in nonlinear fashion at the time of signal acquisition. The linearity is restored in the PLL behavior once acquisition is over and signal tracking is taking place. But the same PLL or DSP-DPLL shows non-linearity both during acquisition and tracking when narrowband channel interference is present in the received signal. In this paper, a single tone signal is introduced as channel interference to study the effect on DPLL and its modified versions. To overcome the effect of channel interference, a single tone dither signal is included in the loop of DPLL. Although an improvement in acquisition and tracking performance is observed, but addition of dither signal contributes to the phase error variance and consequently output noise to increase. Therefore, a further modification is proposed by incorporating an additional phase control in the digital control oscillator (DCO) of the loop to improve the output SNR. The proposed loop is implemented on reconfigurable logic platform using System Generator, a tool from Xilinx used to design real time DSP application. The hardware simulation results demonstrate a comparison among traditional DPLL, dithered DPLL and phase controlled dithered DPLL where the proposed version of the loop outperforms others in terms of acquisition and noise rejection. Keywords DSP Digital Phase Locked Loop, Phase Controlled DPLL, Channel Interference, Dither DPLL, VHDL System Design, Modified DCO
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KONDRATENKO, L. A., L. I. MIRONOVA, V. G. DMITRIEV, O. V. EGOROVA, and A. O. SHEMIAKOV. "INVESTIGATION OF THE DYNAMICS OF NONLINEAR MECHANICAL SYSTEMS WITH LONG POWER LINES THROUGH DIGITAL MODELING." Periódico Tchê Química 16, no. 33 (March 20, 2019): 668–80. http://dx.doi.org/10.52571/ptq.v16.n33.2019.683_periodico33_pgs_668_680.pdf.
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Many of the mechanisms used in industry contain input and output links connected by long lines of force. Increasing the efficiency and service life of mechanical systems with long lines is of great importance for the country's economy. For a more rational use of these devices, it is important to maintain these operating modes with maximum accuracy, usually including the required speed of the actuator and the voltage in the lines. Such parameters can spontaneously change depending on the operating conditions of the system. In the presence of various influences, similar tasks to determine the marked regimes and parameters indicating the need for their change can be solved only with the help of the corresponding theory and research methods. The article presents the problems and the method of studying two-tier mechanical systems with an infinite number of degrees of freedom on the basis of the equations of momentum and moment of momentum in differential form. Transformations with the use of well-known wave equations are proposed, which made it possible to explicitly take into account the oscillations of the speeds of motion and stresses in the force lines of mechanical systems when describing dynamic processes. The solution of systems of partial differential equations is given using the Laplace transform, which made it possible to obtain general equations of motion and, after some simplifications, proceed to ordinary differential equations that take into account the dynamic features of systems with distributed parameters. The modernized Runge-Kutta method obtained solutions and carried out numerical simulation of transient processes in the hydraulic drive, the results of which have good convergence with full-scale experiments.
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Beal, Aubrey N., and Robert N. Dean. "A Random Stimulation Source for Evaluating MEMS Devices using an Exact Solvable Chaotic Oscillator." Additional Conferences (Device Packaging, HiTEC, HiTEN, and CICMT) 2015, DPC (January 1, 2015): 001594–625. http://dx.doi.org/10.4071/2015dpc-wp32.
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MEMS devices are nearly ubiquitous, with applications ranging from automobiles to toys, medical equipment to missiles, and cell phones to industrial equipment. At the microscale, fabrication tolerances are significantly less precise than at the scale of traditional machining techniques. This can result in significant differences in the operating characteristics between otherwise identical MEMS devices. A wide bandwidth random excitation source is ideal for evaluating these components, whether used as the forcing function for an electromechanical shaker employed to measure transmissibility, or as a voltage source to evaluate actuator structure resonances and instabilities. An electronic chaotic oscillator provides an ideal wide bandwidth voltage source which is provably random from first principles and may be simply integrated for the aforementioned MEMS testing. This type of system is easily integrated through standard Si MEMS processes and readily lends itself to application as a built-in-self test (BIST) component. These systems guarantee uniform frequency content from D.C. up to 100kHz due to their characteristically random behavior and serve as a strong candidate for providing uniform spectral density to a device under test. The proposed system is a simple, electronic circuit that creates a random, wideband excitation voltage for observing characteristics of MEMS devices. This functionality is achieved by the analog, digital or mixed signal computation of nonlinear differential equations that describe various exactly solvable chaotic systems. By creating Si microsystems which perform these computations, these test sources may be readily fabricated as integrated BIST components for MEMS devices or fabricated separately and integrated by flip chip assembly techniques. Furthermore, by considering the iterated map of this particular category of stimulation source, a direct and easy measurement of the stimulation entropy may be monitored and corrected. This work begins as a theoretical treatment involving the Nonlinear Dynamics of these types of systems including chaotic systems which permit closed form solutions. These systems are described classically through nonlinear differential equations and intuitively through iterated maps. These techniques reveal inherent methods for entropy measurement in these sources which may be implemented and controlled easily using electronic circuits. Subsequently, the simulation, circuit design methodology, circuit simulation, fabrication, testing and hardware verification of these wideband chaotic sources is presented. The development of this work delineates simple, wideband electronic testing circuits which may be fully integrated with MEMS devices using standard Si MEMS processes. The resulting microsystem may be used as the forcing function when measuring transmissibility of MEMS devices, or as a BIST element to evaluate MEMS microstructure characteristics through direct microelectronic fabrication or flip chip integration.
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Noskov, V. Ya, E. V. Bogatyrev, K. A. Ignatkov, and K. D. Shaidurov. "Features of the Formation and Processing of Signals in an Autodyne Radar with Frequency Modulation Taking into Account the Nonlinearity of the Modulation Characteristic." Ural Radio Engineering Journal 5, no. 2 (2021): 119–43. http://dx.doi.org/10.15826/urej.2021.5.1.003.
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The results of the study of the features of the formation and processing of signals of autodyne short-range radar systems (SRR) with frequency modulation (FM) involving non-linearity of the modulation characteristic are presented. The numerical simulation of the nonlinear influence of the modulation characteristic on the shape and spectrum of the autodyne signal is implemented on the basis of the mathematical model of the autodyne generator. We have established that even a small non-linearity of this characteristic causes a significant distortion of the shape and spectrum of the autodyne signal. A method of quasi-static correction of the law of frequency modulation of probing radiation using a digital signal processor is proposed, which does not require complication of the microwave part of the autodyne SRR with FM. The results of experimental studies of an 8-mm autodyne SRR made on the basis of a Gann diode oscillator with frequency control by varicap are presented.
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Lytviak, Oleksandr, Vasyl Loginov, Sergii Komar, and Yevhen Martseniuk. "Self-Oscillations of The Free Turbine Speed in Testing Turboshaft Engine with Hydraulic Dynamometer." Aerospace 8, no. 4 (April 17, 2021): 114. http://dx.doi.org/10.3390/aerospace8040114.
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Self-oscillations are one of the common problems in the complex automatic system, that can occur due to the features of the workflow and the design of the governor. The development of digital control systems has made it possible to damp self-oscillations by applying complex control laws. However, for hydromechanical systems, such way is unacceptable due to the design complexity and the governor cost. The objective of this work is to determine the parameters of the hydromechanical free turbine speed controller, ensuring the absence of self-oscillations during ground tests of the turboshaft engine with a hydraulic dynamometer. The TV3-117VM engine (Ukraine) with the NR-3VM regulator pump (Ukraine) was selected as the object of the study. However, self-oscillations can also occur in any modifications of the TV3-117 engine with any NR-3 regulator pump. The results of the research may be of interest to engineers and scientists who investigate the dynamics of automatic control systems for similar engines. The paper analyses the nonlinear features of the empirical characteristics of the FTSC leading to self-oscillations of the engine speed. The authors propose the mathematical model of the automatic control system dynamics, which takes into account all the features of the engine and regulator pump. It is shown that the load characteristics of the water brake and the helicopter main rotor can differ significantly. Research of the dynamic characteristics of the TV3-117VM engine was carried out. The analysis showed a good agreement between the calculation results and the field test results, and made it possible to determine the parameters of the controller, which lead to self-oscillations during test. Two cases are considered. The first case includes ground tests of the engine with a water brake; the second case—flight tests of the engine as part of the helicopter’s power plant. The data obtained make it possible to develop recommendations for adjusting the hydromechanical governor without testing it on the engine.
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Gribova, О. V., I. V. Merkuriyev, M. R. Saipulayev, and V. P. Chirkov. "Developing a Mathematical Model of a Micromechanical Sensor for Inertial Information." Rocket-space device engineering and information systems 9, no. 1 (2022): 97–102. http://dx.doi.org/10.30894/issn2409-0239.2022.9.1.97.102.
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Creating an integrated system of orientation and navigation of small spacecraft based on precision sensors of inertial and external information is an urgent task for the space industry. The object of research is a micromechanical gyroscope (MMG) with a gimbal suspension of a sensitive element. The problem of increasing the accuracy of the MMG by building a new mathematical model of the sensor accurate enough to take into account the influence of technological errors of manufacturing and nonlinear nonstationary effects associated with finite oscillations of a sensitive element and slow change in system parameters. To build a digital model of the micromechanical inertial information sensor, parametric design systems have been applied enabling a full cycle of design documentation creation and calculations. The parametric calculations of the structural scheme were used to analyze the stress-strain state of mechanical elements under various external influences including extreme overloads. The obtained mathematical model was supplemented by analytical methods of nonlinear mechanics, which allow taking into account the influence of finite vibrations of structural elements on the dynamics and accuracy of measurements of angular motion of the gyroscope base. The results of bench experimental tests of sensors carried out to check the adequacy of the developed numerical mathematical model are discussed.
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Rasool, Akhtar, Esref Emre Ozsoy, Fiaz Ahmad, Asif Sabanoviç, and Sanjeevikumar Padmanaban. "Disturbance-observer based control of voltage-source-converter under unbalanced voltage conditions." World Journal of Engineering 14, no. 6 (December 4, 2017): 522–31. http://dx.doi.org/10.1108/wje-01-2017-0021.
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Purpose This paper aims to propose a novel grid current control strategy for grid-connected voltage source converters (VSCs) under unbalanced grid voltage conditions. Design/methodology/approach A grid voltage dynamic model is represented in symmetrical positive and negative sequence reference frames. A proportional controller structure with a first-order low-pass filter disturbance observer (DOB) is designed for power control in unbalanced voltage conditions. This controller is capable of meeting the positive sequence power requirements, and it also eliminates negative sequence power components which cause double-frequency oscillations on power. The symmetrical components are calculated by using the second-order generalized integrator-based observer, which accurately estimates the symmetrical components. Findings Proportional current controllers are sufficient in this study in a wide range of operating conditions, as DOB accurately estimates and feed-forwards nonlinear terms which may be deteriorated by physical and operating conditions. This is the first reported scheme which estimates the VSC disturbances in terms of symmetrical component decomposition and the DOB concept. Originality/value The proposed method does not require any grid parameter to be known, as it estimates nonlinear terms with a first-order low-pass filter DOB. The proposed control system is implemented on a dSPACE ds1103 digital controller by using a three-phase, three-wire VSC.
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Novembre, Giacomo, Manuel Varlet, Shujau Muawiyath, Catherine J. Stevens, and Peter E. Keller. "The E-music box: an empirical method for exploring the universal capacity for musical production and for social interaction through music." Royal Society Open Science 2, no. 11 (November 2015): 150286. http://dx.doi.org/10.1098/rsos.150286.
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Humans are assumed to have a natural—universal—predisposition for making music and for musical interaction. Research in this domain is, however, typically conducted with musically trained individuals, and therefore confounded with expertise. Here, we present a rediscovered and updated invention—the E-music box—that we establish as an empirical method to investigate musical production and interaction in everyone. The E-music box transforms rotatory cyclical movements into pre-programmable digital musical output, with tempo varying according to rotation speed. The user’s movements are coded as continuous oscillatory data, which can be analysed using linear or nonlinear analytical tools. We conducted a proof-of-principle experiment to demonstrate that, using this method, pairs of non-musically trained individuals can interact according to conventional musical practices (leader/follower roles and lower-pitch dominance). The results suggest that the E-music box brings ‘active’ and ‘interactive’ musical capacities within everyone’s reach. We discuss the potential of this method for exploring the universal predisposition for music making and interaction in developmental and cross-cultural contexts, and for neurologic musical therapy and rehabilitation.
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Dubcek, Tena, Daniel Moreno-Garcia, Luis Guillermo Villanueva, Dirk-Jan van Manen, Johan Robertsson, and Marc Serra Garcia. "Metamaterials you can talk to: Speech recognition with elastic neural networks." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A129. http://dx.doi.org/10.1121/10.0010873.
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To detect spoken commands, smart devices (for example, a speaker with Alexa or Siri) continuously convert acoustic waves to electronic signals, translate them into the digital domain, and analyze them in a signal processor. Each of these steps constantly consumes energy, imposing the need for tethered operation or large batteries. We propose to solve this problem using elastic neural networks, metamaterials consisting of arrays of coupled (potentially nonlinear) resonators. The frequencies and couplings of the resonators are optimized to maximise the speech classification accuracy (energy transmitted when excited with one word but not another). Even in purely linear metastructures, we observe binary classification accuracies exceeding 90% for a large number of pairs of words. This is demonstrated on a dataset from a large and diverse group of speakers. To attain these results, we have developed refined modelling techniques involving localised oscillations and machine learning. A unique feature of metamaterial-based speech processing is that speech classification is entirely passive, requiring no external energy. This is possible due to the very low energy dissipation of elastic waves.
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AKHMETOV, S., N. AKHMETOV, and S. ABUGALYEV. "MODELING THE STABILITY OF DRILL STRINGS AT THE DESIGN STAGE IS ONE OF THE METHODS FOR PREDICTING THE RELIABILITY OF THEIR OPERATION." Neft i gaz 5, no. 119 (April 15, 2020): 84–95. http://dx.doi.org/10.37878/2708-0080/2020-5.029.
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In the address of the Head of state Kassym-Jomart Tokayev to the people of Kazakhstan, announced on September 1, 2020, a number of tasks related to improving the productivity of industrial production, including the oil industry, with the broad introduction of modern IT technologies. This is evidenced by the instruction of the President sent in his Message to the Western regions of the country on issues of investment attraction for construction in the future, petrochemical complexes and creating new production runs of high value added [1]. This requires in the near future expand the set of activities for finding and developing new oil and gas fields, and in line with this, a substantial increase in drilling operations, the introduction of effective methods of deep drilling. In this regard, it is very important to ensure the reliability of drilling systems (DS) at the design stage. This, in turn, allows you to solve several tasks simultaneously: based on the use of modeling methods and digital technologies, predict the performance and working properties of DS elements in advance, before they are created, and thereby significantly reduce the risks of large capital expenditures, human and time resources, which would have acquired an irreversible process already at the stage of operation; create digital technology platforms that can become the driving force of the digital ecosystem of the industry [1], in our case, drilling and exploitation of oil and gas fields, thus complementing the electronic database with information about problem situations and effective methods of their solution (elimination). In this paper, which is a continuation of the results of the authors ' research published in [2], we consider special cases of modeling the stability and vibration of drill strings (DStr) taking into account the geometric nonlinearity of deformation. Such cases are buckling often occur with increasing depth of drilling, i.e., length, DStr, where the system becomes quite like a long stretchedcompressed tubular rods under longitudinal and transverse loads. In order to study (predict) the reliability of DS in such situations, the dynamic stability of a geometrically nonlinear DStr under variable loads is investigated, and a method for applying the finite element method to study the dynamic stability of DStr under geometric nonlinearity of their deformation is proposed. To study these phenomena under DStr loading conditions, the authors of this article consider the dynamic stability of a weighed column, taking into account its physical nonlinearity under compressive loads of time variables. Based on the analysis of the obtained theoretical dependencies, the DStr deflections are compared for both physically linear and nonlinear problems. It is established that taking into account physical nonlinearity leads to an oscillatory process with a limited amplitude, and that the presence of nonlinearity for the selected parameters leads to an oscillatory process of the column. In General, the graphical dependencies that characterize the DStr stability parameters obtained on the basis of mathematical modeling methods demonstrate the ability to predict and control the Parameters of this process at the design stage, which allows us to estimate the most optimal zones (limits, ranges) that ensure the efficiency and reliability of the DS operation by varying their values in advance.
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Ubertini, F., F. Comodini, A. Fulco, and M. Mezzi. "A Simplified Parametric Study on Occupant Comfort Conditions in Base Isolated Buildings under Wind Loading." Advances in Civil Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/3524975.
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Vibrations in buildings can cause occupant discomfort in the form of annoyance, headache, or sickness. While occupant comfort is considered in international standards regarding the design of high rise buildings against wind loading, it is neglected in the design of buildings with seismic protective base isolation systems. Nevertheless, due to their low flexibility, base isolated buildings can be prone to wind-induced vibrations, which makes occupant discomfort a potentially significant serviceability limit state. This paper presents a study on occupant comfort conditions in wind-excited base isolated buildings. A numerical simplified parametric procedure is proposed in order to evaluate the return period of wind events causing human discomfort. A parametric investigation is then presented to evaluate the effects of salient parameters on comfort conditions. The procedure is based on (i) the nonlinear dynamic analysis of the structure modeled as a single-degree-of-freedom oscillator with hysteretic base isolators, (ii) the digital generation of time histories of turbulent wind velocity, and (iii) comfort evaluations based on international standards. Results demonstrate that discomfort conditions can occur a few times in a year, depending upon the wind-exposure of the site, what suggests considering this serviceability limit state in the design of base isolated buildings.
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Bryukhanov, Yu A., M. V. Lebedev, A. L. Priorov, and D. V. Rudykh. "Oscillations in autonomous two-dimensional second-order recursive digital systems with symmetric coefficients and binary quantization." Radiophysics and Quantum Electronics 49, no. 7 (July 2006): 572–78. http://dx.doi.org/10.1007/s11141-006-0091-4.
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Lin Deng, Mao, and Wei Qiu Zhu. "Responses of Linear and Nonlinear Oscillators to Fractional Gaussian Noise With Hurst Index Between 1/2 and 1." Journal of Applied Mechanics 82, no. 10 (July 22, 2015). http://dx.doi.org/10.1115/1.4031009.
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The responses of linear and nonlinear oscillators to fractional Gaussian noise (fGn) are studied. First, some preliminary concepts and properties of fractional Brownian motion (fBm) and fGn with Hurst index 1/2<H<1 are introduced. Then, the exact sample solution, correlation function, spectral density, and mean-square value of the response of linear oscillator to fGn are obtained. Based on the sample solution, it is proved that the long-range correlation index of displacement response of linear oscillator is the same as that of excitation fGn, i.e., 2-2H, while the velocity response has no such long-range correlation. An interesting discovery is that the ratio of kinetic energy to total energy decreases as increasing Hurst index H. Finally, for the responses of one and two degrees-of-freedom (DOF) nonlinear oscillators to fGn, the equivalent linearization method is applied to obtain the sample functions, correlation functions and mean-square values of the responses. Plenty of digital simulation results are obtained to support these solutions. It is shown that the approximate solution is effective for weakly nonlinear oscillators and it is feasible to apply the equivalent linearization to study multi-DOF weakly nonlinear oscillators.
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Ishimura, Kazuyoshi, Ryota Inden, Naoto Komeno, and Isao T. Tokuda. "Asymmetric Entrainment Structure of Pierce Oscillator Circuit." Journal of Circuits, Systems and Computers, August 27, 2020, 2150066. http://dx.doi.org/10.1142/s0218126621500663.
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Experimental study is presented to uncover entrainment property of Pierce oscillator circuit (i.e., one of the most standard circuits for crystal oscillators) subject to sinusoidal external forcing. In contrast to the well-known Arnold tongues observed in a wide class of forced nonlinear systems, asymmetric shape was observed as an entrainment region of the circuit in two-dimensional parameter space spanned by the external forcing strength and frequency. Computation of the impedance curve revealed that the asymmetric shape is due to positive (inductive) or negative (capacitive) reactance of the Pierce circuit, which facilitates or inhibits the circuit oscillations. We extend this insight into two coupled Pierce circuits and show that, to efficiently achieve their synchronization, it is advantageous to drive a slow oscillator circuit by a fast circuit rather than to drive a fast circuit by a slow circuit. Our study provides a guideline on an optimal network configuration for coupled crystal oscillators, which may find applications in distributed digital clocks and wireless communication systems.
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Kong, Chen, Zhen Chen, and Xian-Bin Liu. "On the Stochastic Dynamical Behaviors of a Nonlinear Oscillator Under Combined Real Noise and Harmonic Excitations." Journal of Computational and Nonlinear Dynamics 12, no. 3 (December 5, 2016). http://dx.doi.org/10.1115/1.4034735.
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The exit problem and global stability of a nonlinear oscillator excited by an ergodic real noise and harmonic excitations are examined. The real noise is assumed to be a scalar stochastic function of an n-dimensional Ornstein–Uhlenbeck vector process which is the output of a linear filter system. Due to the existence of t-dependent excitation, two two-dimensional Fokker–Planck–Kolmogorov (FPK) equations governing the van der Pol variables process and the amplitude-phase process, respectively, are obtained and discussed through a perturbation method and the spectrum representations of the FPK operator and its adjoint operator of the linear filter system, while the detailed balance condition and the strong mixing condition are removed. Based on these FPK equations, the global properties of one-dimensional nonlinear oscillators with external or (and) internal periodic excitations under external or (and) internal real noises can be examined. Finally, a Duffing oscillator excited by a parametric real noise and parametric harmonic excitations is presented as an example, and the mean first-passage time (MFPT) about the oscillator's exit behavior between limit cycles is obtained under both wide-band noise and narrow-band noise excitations. The analytical result is verified by digital simulation.
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Wu, Y. J., and H. Y. Wang. "First-Crossing Problem of Weakly Coupled Strongly Nonlinear Oscillators Subject to a Weak Harmonic Excitation and Gaussian White Noises." Journal of Vibration and Acoustics 140, no. 4 (February 23, 2018). http://dx.doi.org/10.1115/1.4039244.
Full textAbstract:
We study first-crossing problem of two-degrees-of-freedom (2DOF) strongly nonlinear mechanical oscillators analytically. The excitation is the combination of a deterministic harmonic function and Gaussian white noises (GWNs). The generalized harmonic function is used to approximate the solutions of the original equations. Four cases are studied in terms of the types of resonance (internal or external or both). For each case, the method of stochastic averaging is used and the stochastically averaged Itô equations are obtained. A backward Kolmogorov (BK) equation is set up to yield the failure probability and a Pontryagin equation is set up to yield average first-crossing time (AFCT). A 2DOF Duffing-van der Pol oscillator is chosen as an illustrative example to demonstrate the effectiveness of the analytical method. Numerically analytical solutions are obtained and validated by digital simulation. It is shown that the proposed method has high efficiency while still maintaining satisfactory accuracy.
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"Nonlinear oscillations and chaos from digital filter overflow." Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences 353, no. 1701 (October 16, 1995): 85–99. http://dx.doi.org/10.1098/rsta.1995.0092.
Full textAbstract:
Nonlinear digital-filter overflow-oscillations arising from two’s complement arithmetic are described with the emphasis on explaining the reasons for the behaviour and providing illustrations of typical oscillations. The complex properties of some of these oscillations have led to extensive investigations of the nonlinear dynamics and to proposals for applications. The paper provides an introduction to the published literature on this subject.