Academic literature on the topic 'Digital Nonlinear Oscillators'
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Journal articles on the topic "Digital Nonlinear Oscillators"
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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.
Dissertations / Theses on the topic "Digital Nonlinear Oscillators"
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MORETTI, RICCARDO. "Digital Nonlinear Oscillators: A Novel Class of Circuits for the Design of Entropy Sources in Programmable Logic Devices." Doctoral thesis, Università di Siena, 2021. http://hdl.handle.net/11365/1144376.
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In recent years, cybersecurity is gaining more and more importance. Cryptography is used in numerous applications, such as authentication and encryption of data in communications, access control to restricted or protected areas, electronic payments. It is safe to assume that the presence of cryptographic systems in future technologies will become increasingly pervasive, leading to a greater demand for energy efficiency, hardware reliability, integration, portability, and security.
However, this pervasiveness introduces new challenges: the implementation of conventional cryptographic standards approved by NIST requires the achievement of performance in terms of timing, chip area, power and resource consumption that are not compatible with reduced complexity hardware devices, such as IoT systems. In response to this limitation, lightweight cryptography comes into play - a branch of cryptography that provides tailor-made solutions for resource-limited devices.
One of the fundamental classes of cryptographic hardware primitives is represented by Random Number Generators (RNGs), that is, systems that provide sequences of integers that are supposed to be unpredictable.
The circuits and systems that implement RNGs can be divided into two categories, namely Pseudo Random Number Generators (PRNGs) and True Random Number Generators (TRNGs).
PRNGs are deterministic and possibly periodic finite state machines, capable of generating sequences that appear to be random. In other words, a PRNG is a device that generates and repeats a finite random sequence, saved in memory, or generated by calculation.
A TRNG, on the other hand, is a device that generates random numbers based on real stochastic physical processes. Typically, a hardware TRNG consists of a mixed-signal circuit that is classified according to the stochastic process on which it is based. Specifically, the most used sources of randomness are chaotic circuits, high jitter oscillators, circuits that measure other stochastic processes.
A chaotic circuit is an analog or mixed-signal circuit in which currents and voltages vary over time based on certain mathematical properties. The evolution over time of these currents and voltages can be interpreted as the evolution of the state of a chaotic nonlinear dynamical system.
Jitter noise can instead be defined as the deviation of the output signal of an oscillator from its true periodicity, which causes uncertainty in its low-high and high-low transition times.
Other possible stochastic processes that a TRNG can use may involve radioactive decay, photon detection, or electronic noise in semiconductor devices.
TRNG proposals presented in the literature are typically designed in the form of Application Specific Integrated Circuits (ASICs). On the other hand, in recent years more and more researchers are exploring the possibility of designing TRNGs in Programmable Logic Devices (PLDs). A PLD offers, compared to an ASIC, clear advantages in terms of cost and versatility. At the same time, however, there is currently a widespread lack of trust in these PLD-based architectures, particularly due to strong cryptographic weaknesses found in Ring Oscillator-based solutions.
The goal of this thesis is to show how this mistrust does not depend on poor performance in cryptographic terms of solutions for the generation of random numbers based on programmable digital technologies, but rather on a still immature approach in the study of TRNG architectures designed on PLDs.
During the thesis chapters a new class of nonlinear circuits based on digital hardware is introduced that can be used as entropy sources for TRNGs implemented in PLDs, identified by the denomination of Digital Nonlinear Oscillators (DNOs).
In Chapter 2 a novel class of circuits that can be used to design entropy sources for True Random Number Generation, called Digital Nonlinear Oscillators (DNOs), is introduced. DNOs constitute nonlinear dynamical systems capable of supporting complex dynamics in the time-continuous domain, although they are based on purely digital hardware. By virtue of this characteristic, these circuits are suitable for their implementation on Programmable Logic Devices. By focusing the analysis on Digital Nonlinear Oscillators implemented in FPGAs, a preliminary comparison is proposed between three different circuit topologies referable to the introduced class, to demonstrate how circuits of this type can have different characteristics, depending on their dynamical behavior and the hardware implementation.
In Chapter 3 a methodology for the analysis and design of Digital Nonlinear Oscillators based on the evaluation of their electronics aspects, their dynamical behavior, and the information they can generate is formalized. The presented methodology makes use of different tools, such as figures of merit, simplified dynamical models, advanced numerical simulations and experimental tests carried out through implementation on FPGA. Each of these tools is analyzed both in its theoretical premises and through explanatory examples.
In Chapter 4 the analysis and design methodologies of Digital Nonlinear Oscillators formalized in Chapter 3 are used to describe the complete workflow followed for the design of a novel DNO topology. This DNO is characterized by chaotic dynamical behaviors and can achieve high performance in terms of generated entropy, downstream of a reduced hardware complexity and high sampling frequencies. By exploiting the simplified dynamical model, the advanced numerical simulations in Cadence Virtuoso and the FPGA implementation, the presented topology is extensively analyzed both from a theoretical point of view (notable circuit sub-elements that make up the topology, bifurcation diagrams, internal periodicities) and from an experimental point of view (generated entropy, source autocorrelation, sensitivity to routing, application of standard statistical tests).
In Chapter 5 an algorithm, called Maximum Worst-Case Entropy Selector (MWCES), that aims to identify, within a set of entropy sources, which offers the best performance in terms of worst-case entropy, also known in literature as "min-entropy", is presented. This algorithm is designed to be implemented in low-complexity digital architectures, suitable for lightweight cryptographic applications, thus allowing online maximization of the performance of a random number generation system based on Digital Nonlinear Oscillators. This chapter presents the theoretical premises underlying the algorithm formulation, some notable examples of its generic application and, finally, considerations related to its hardware implementation in FPGA.
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Ing, James. "Near grazing dynamics of piecewise linear oscillators." Thesis, Available from the University of Aberdeen Library and Historic Collections Digital Resources, 2008. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=24711.
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Akre, Niamba Jean-Michel. "Etude de la synchronisation et de la stabilité d’un réseau d’oscillateurs non linéaires. Application à la conception d’un système d’horlogerie distribuée pour un System-on-Chip (projet HODISS)." Thesis, Supélec, 2013. http://www.theses.fr/2013SUPL0001/document.
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Le projet HODISS dans le cadre duquel s'effectue nos travaux adresse la problématique de la synchronisation globale des systèmes complexes sur puce (System-on-Chip ou SOCs, par exemple un multiprocesseur monolithique). Les approches classiques de distribution d'horloges étant devenues de plus en plus obsolètes à cause de l'augmentation de la fréquence d'horloge, l'accroissement des temps de propagation, l'accroissement de la complexité des circuits et les incertitudes de fabrication, les concepteurs s’intéressent (pour contourner ces difficultés) à d'autres techniques basées entre autres sur les oscillateurs distribués. La difficulté majeure de cette dernière approche réside dans la capacité d’assurer le synchronisme global du système. Nous proposons un système d'horlogerie distribuée basé sur un réseau d’oscillateurs couplés en phase. Pour synchroniser ces oscillateurs, chacun d'eux est en fait une boucle à verrouillage de phase qui permet ainsi d'assurer un couplage en phase avec les oscillateurs des zones voisines. Nous analysons la stabilité de l'état synchrone dans des réseaux cartésiens identiques de boucles à verrouillage de phase entièrement numériques (ADPLLs). Sous certaines conditions, on montre que l'ensemble du réseau peut synchroniser à la fois en phase et en fréquence. Un aspect majeur de cette étude réside dans le fait que, en l'absence d'une horloge de référence absolue, le filtre de boucle dans chaque ADPLL est piloté par les fronts montants irréguliers de l'oscillateur local et, par conséquent, n'est pas régi par les mêmes équations d'état selon que l'horloge locale est avancée ou retardée par rapport au signal considéré comme référence. Sous des hypothèses simples, ces réseaux d'ADPLLs dits "auto-échantillonnés" peuvent être décrits comme des systèmes linéaires par morceaux dont la stabilité est notoirement difficile à établir. L'une des principales contributions que nous présentons est la définition de règles de conception simples qui doivent être satisfaites sur les coefficients de chaque filtre de boucle afin d'obtenir une synchronisation dans un réseau cartésien de taille quelconque. Les simulations transitoires indiquent que cette condition nécessaire de synchronisation peut également être suffisante pour une classe particulière d'ADPLLs "auto-échantillonnés"The HODISS project, context in which this work is achieved, addresses the problem of global synchronization of complex systems-on-chip (SOCs, such as a monolithic multiprocessor). Since the traditional approaches of clock distribution are less used due to the increase of the clock frequency, increased delay, increased circuit complexity and uncertainties of manufacture, designers are interested (to circumvent these difficulties) to other techniques based among others on distributed synchronous clocks. The main difficulty of this latter approach is the ability to ensure the overall system synchronization. We propose a clock distribution system based on a network of phase-coupled oscillators. To synchronize these oscillators, each is in fact a phase-locked loop which allows to ensure a phase coupling with the nearest neighboring oscillators. We analyze the stability of the synchronized state in Cartesian networks of identical all-digital phase-locked loops (ADPLLs). Under certain conditions, we show that the entire network may synchronize both in phase and frequency. A key aspect of this study lies in the fact that, in the absence of an absolute reference clock, the loop-filter in each ADPLL is operated on the irregular rising edges of the local oscillator and consequently, does not use the same operands depending on whether the local clock is leading or lagging with respect to the signal considered as reference. Under simple assumptions, these networks of so-called “self-sampled” all-digital phase-locked-loops (SS-ADPLLs) can be described as piecewise-linear systems, the stability of which is notoriously difficult to establish. One of the main contributions presented here is the definition of simple design rules that must be satisfied by the coefficients of each loop-filter in order to achieve synchronization in a Cartesian network of arbitrary size. Transient simulations indicate that this necessary synchronization condition may also be sufficient for a specific class of SS-ADPLLs
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Mansingka, Abhinav S. "Fully Digital Chaotic Oscillators Applied to Pseudo Random Number Generation." Thesis, 2012. http://hdl.handle.net/10754/224712.
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This thesis presents a generalized approach for the fully digital design and implementation
of chaos generators through the numerical solution of chaotic ordinary
differential equations. In particular, implementations use the Euler approximation
with a fixed-point twos complement number representation system for optimal hardware
and performance. In general, digital design enables significant benefits in terms
of power, area, throughput, reliability, repeatability and portability over analog implementations
of chaos due to lower process, voltage and temperature sensitivities and
easy compatibility with other digital systems such as microprocessors, digital signal
processing units, communication systems and encryption systems. Furthermore, this
thesis introduces the idea of implementing multidimensional chaotic systems rather
than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures
that provide significant performance and area benefits.
This work focuses efforts on the well-understood family of autonomous 3rd order
"jerk" chaotic systems. The effect of implementation precision, internal delay cycles
and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes
of operation. Enhanced chaos generators that exploit long-term divergence in two
identical systems of different precision are also explored. Digital design is shown to
enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic
systems, essentially creating non-autonomous chaos that has thus far been difficult
to implement in the analog domain.
Seven different systems are mathematically assessed for chaotic properties, implemented
at the register transfer level in Verilog HDL and experimentally verified
on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously
studied using the NIST SP. 800-22 statistical testing suite. The output is adapted
for pseudo random number generation by truncating statistically defective bits. Finally,
a novel post-processing technique using the Fibonacci series is proposed and
implemented with a non-autonomous driven hyperchaotic system to provide pseudo
random number generators with high nonlinear complexity and controllable period
length that enables full utilization of all branches of the chaotic output as statistically
secure pseudo random output.
Book chapters on the topic "Digital Nonlinear Oscillators"
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Addabbo, Tommaso, Ada Fort, Riccardo Moretti, Marco Mugnaini, and Valerio Vignoli. "Low-Level Advanced Design of True Random Number Generators Based on Truly Chaotic Digital Nonlinear Oscillators in FPGAs." In Lecture Notes in Electrical Engineering, 180–86. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95498-7_25.
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Rubio, M. A., M. de la Torre, J. C. Antoranz, and M. G. Velarde. "Digital and Analog Approach to Intermittencies and 1/f Noise in a Nonlinear Helmholtz Oscillator." In Springer Series in Synergetics, 196–201. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-73089-4_17.
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Epstein, Irving R., and John A. Pojman. "Computational Tools." In An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.003.0012.
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It is fair to say that the field of nonlinear chemical dynamics would not be where it is today, and perhaps it would not exist at all, without fast digital computers. As we saw in Chapter 1, the numerical simulation of the essential behavior of the BZ reaction (Edelson et al., 1975) did much both to support the FKN mechanism and to make credible the idea that chemical oscillators could be understood without invoking any new principles of chemical kinetics. In 1975, solving those differential equations challenged the most advanced machines of the day, yet the computers used then were less powerful than many of today’s home computers! Despite the present widespread availability of computing power, there remain many challenging computational problems in nonlinear dynamics, and even seemingly simple equations can be difficult to solve or maybe even lead to spurious results. In this chapter, we will look at some of the most widely used computational techniques, try to provide a rudimentary understanding of how the methods work (and how they can fail!), and list some of the tools that are available. There are several reasons for utilizing the techniques described in this chapter: 1. For a complicated system, it is generally not possible to measure all of the rate constants in a proposed mechanism. One way to estimate the remaining parameters is to simulate numerically the behavior of the system, varying the unknown rate constants until the model satisfactorily reproduces the experimental behavior. 2. If a mechanism, which may consist of dozens of elementary chemical reactions, is valid, then it should reproduce the observed dynamical behavior. Proposed mechanisms are most commonly tested by integrating the corresponding rate equations numerically and comparing the results with the experimental time series, or by comparing the results of many such simulations with different initial conditions (or of a numerical continuation study) to the experimental phase diagram. 3. Numerical results can act as a guide to further experiments. The real reason for developing models is not to interpolate between our experimental observations but to extrapolate into unknown realms.
Conference papers on the topic "Digital Nonlinear Oscillators"
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Addabbo, T., A. Fort, R. Moretti, M. Mugnaini, and V. Vignoli. "Analysis of a Circuit Primitive for the Reliable Design of Digital Nonlinear Oscillators." In 2019 15th Conference on Ph.D Research in Microelectronics and Electronics (PRIME). IEEE, 2019. http://dx.doi.org/10.1109/prime.2019.8787773.
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Rontani, D., A. Locquet, M. Sciamanna, and D. S. Citrin. "Multiplexing digital information using hyperchaotic optoelectronic oscillators with nonlinear time-delayed feedback loops." In 11th European Quantum Electronics Conference (CLEO/EQEC). IEEE, 2009. http://dx.doi.org/10.1109/cleoe-eqec.2009.5194738.
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Zaycev, Valeriy, and Alalvan Kasim. "NON-LINEAR OSCILLATORS IN DISCRETE TIME: ANALYSIS AND SYNTHESIS OF DYNAMIC SYSTEMS." In CAD/EDA/SIMULATION IN MODERN ELECTRONICS 2021. Bryansk State Technical University, 2021. http://dx.doi.org/10.30987/conferencearticle_61c997ef87b033.35809465.
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A physically justified method of synthesis of nonlinear oscillating systems oscillating in discrete time (DT) is proposed. Synthesized dynamic systems are used as nonlinear discrete (digital) filters and basic models of radio system elements.
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Addabbo, T., A. Fort, M. Mugnaini, V. Vignoli, and M. Garcia-Bosque. "Digital Nonlinear Oscillators in PLDs: Pitfalls and Open Perspectives for a Novel Class of True Random Number Generators." In 2018 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2018. http://dx.doi.org/10.1109/iscas.2018.8351622.
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Addabbo, T., A. Fort, M. Mugnaini, R. Moretti, V. Vignoli, and D. Papini. "A Low-Complexity Method to Address Process Variability in True Random Number Generators based on Digital Nonlinear Oscillators." In 2022 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2022. http://dx.doi.org/10.1109/iscas48785.2022.9937869.
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Nakagami, Takakiyo, and Nobuhiro Fujimoto. "Laser amplifiers for optical signal processing and multiplexing systems." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.wm3.
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The importance of optical signal processing, switching, and multiplexing/demultiplexing in future broadband communication networks has been widely recognized. The huge number of high speed optical signals will be carried by advanced fiber transmission technology such as coherent lightwave systems. Recent progress of laser amplifiers has given researchers an opportunity to exploit new architectures. The power loss due to the many passive elements required for complicated system structures can be minimized by using amplifiers. Nonlinear performances of the laser diodes such as bistability and wavelength conversion characteristics offer a variety of functions, including optical switches, gates, memories, latches, tuned timing oscillators, and wavelength converters. We have developed a photonic access node using bistable laser amplifiers for a "photonic highway" in which signals are processed optically. Drop and insert have been tested with 156-Mbit/s data from/to 622-Mbit/s data streams optically. A prototype optical digital CATV has been developed using the same concept and the desired channel is optically selected from four multiplexed video channel signals.
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Jackson, M. K., M. Y. Frankel, J. F. Whitaker, G. A. Mourou, D. Hulin, A. Antonetti, M. Van Hove, W. De Raedt, P. Crozat, and H. Hafdallah. "Picosecond Pseudomorphic AlGaAs/InGaAs MODFET Large-Signal Switching Measured by Electro-Optic Sampling." In International Conference on Ultrafast Phenomena. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/up.1992.tuc15.
Full textAbstract:
We present a study of the large-signal switching characteristics on a picosecond time scale of an AlGaAs/InGaAs modulation-doped field-effect transistor (MODFET) using electrooptic sampling. The MODFET has been of great interest for high-speed digital and analog applications since its demonstration. Recent progress in the fabrication of such devices has resulted in devices with extrinsic cutoff frequencies exceeding 250GHz, corresponding to response times on the order of a picosecond. The rapid increase in the speed of MODFET devices has outstripped the ability to measure their performance with all-electronic equipment. Devices are most often characterized at lower frequencies and then the results are extrapolated to much higher frequency. These difficulties can be avoided using very high bandwidth optoelectronic techniques based on ultrafast lasers, where it is routine to generate and detect electrical signals with subpicosecond rise and fall times. These optoelectronic techniques have been applied to small-signal characterization of passive coplanar striplines to 1THz and MOD-FET devices to 100GHz. In addition to the very high bandwidth of optoelectronic methods, the ability to generate large electrical signal amplitudes allows the study of switching of active devices. Large-signal characterization of active devices is important because of the wide range of high-speed large-signal device applications, including analog sampling circuits, oscillators, and all digital circuits. It is also important in understanding device operation since large-signal operation on very short time scales involves rapid changes of carrier distributions throughout the device. As the time scale of the signals at the device input and output approaches that required for re-equilibration of carrier distributions, it will become necessary to include these non quasi-static effects in nonlinear device models. Large-signal measurements on a very short time scale will allow the development and verification of nonlinear circuit models, and their comparison with existing models based on bias-dependent small-signal measurements.
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Pranayanuntana, Poramate, and Weerawat Khwankaew. "An Electronically Adjustable Amplitude of OTA-Based Sinusoidal Nonlinear Oscillator." In 2009 International Conference on Digital Image Processing, ICDIP. IEEE, 2009. http://dx.doi.org/10.1109/icdip.2009.24.
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Ricart, J., J. Pons, and M. Dominguez. "Iterative maps for the nonlinear Pulsed Digital Oscillator for MEMS." In 2007 Spanish Conference on Electron Devices. IEEE, 2007. http://dx.doi.org/10.1109/sced.2007.383957.
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Gabrielli, L., M. Giobbi, S. Squartini, and V. Valimaki. "A nonlinear second-order digital oscillator for Virtual Acoustic Feedback." In ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2014. http://dx.doi.org/10.1109/icassp.2014.6855055.
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