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Journal articles on the topic 'Modes oscillatoire'
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1
Cairns, David E., Roland J. Baddeley, and Leslie S. Smith. "Constraints on Synchronizing Oscillator Networks." Neural Computation 5, no. 2 (March 1993): 260–66. http://dx.doi.org/10.1162/neco.1993.5.2.260.
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This paper investigates the constraints placed on some synchronized oscillator models by their underlying dynamics. Phase response graphs are used to determine the phase locking behaviors of three oscillator models. These results are compared with idealized phase response graphs for single phase and multiple phase systems. We find that all three oscillators studied are best suited to operate in a single phase system and that the requirements placed on oscillatory models for operation in a multiple phase system are not compatible with the underlying dynamics of oscillatory behavior for these types of oscillator models.
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Velichko, Andrey, Maksim Belyaev, Vadim Putrolaynen, Alexander Pergament, and Valentin Perminov. "Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks." International Journal of Modern Physics B 31, no. 02 (January 18, 2017): 1650261. http://dx.doi.org/10.1142/s0217979216502611.
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In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.
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Feng, Chunhua. "Dynamic Behavior for a Coupled Nonlinear Oscillator Model with Distributed and Discrete Delays." European Journal of Mathematics and Statistics 2, no. 3 (July 9, 2021): 32–36. http://dx.doi.org/10.24018/ejmath.2021.2.3.43.
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— In this paper, the oscillatory behavior of the solutions for a coupled nonlinear oscillator model with distributed and discrete delays is investigated. Time delay induced partial death patterns with conjugate coupling in relay oscillators has been investigated in the literature. According to the practical problem, the propagation delays are not only the discrete delays, but also with distributed delay. A model includes distributed and discrete delays is considered. By mathematical analysis method, the oscillatory behavior of the coupled nonlinear oscillator model is brought to the instability of the uniqueness equilibrium point and the boundedness of the solutions. Some sufficient conditions are provided to guarantee the oscillation of the solutions. Computer simulations are given to support the present results. Our simulation suggests that the two theorems are only sufficient conditions.
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LABBI, ABDERRAHIM, RUGGERO MILANESE, and HOLGER BOSCH. "ASYMPTOTIC SYNCHRONIZATION IN NETWORKS OF LOCALLY CONNECTED OSCILLATORS." International Journal of Bifurcation and Chaos 09, no. 12 (December 1999): 2279–84. http://dx.doi.org/10.1142/s0218127499001759.
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In this paper, we describe the asymptotic behavior of a network of locally connected oscillators. The main result concerns asymptotic synchronization. The presented study is stated in the framework of neuronal modeling of visual object segmentation using oscillatory correlation. The practical motivations of the synchronization analysis are based on neurophysiological experiments which led to the assumptions that existence of temporal coding schemes in the brain by which neurons, with oscillatory dynamics, coding for the same coherent object synchronize their activities, while neurons coding for different objects oscillate with nonzero phase lags. The oscillator model considered is the FitzHugh–Nagumo neuron model. We restrict our study to the mathematical analysis of a network of such neurons. We firstly show the motivations and suitability of choosing FitzHugh–Nagumo oscillator, mainly for stimulus coding purposes, and then we give sufficient conditions on the coupling parameters which guarantee asymptotic synchronization of oscillators receiving the same external stimulation (input). We have used networks of such oscillators to design a layered architecture for object segmentation in gray-level images. Due to space limitations, description of this architecture and simulation results are briefly referred to by the end of the paper.
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UETA, TETSUSHI, HISAYO MIYAZAKI, TAKUJI KOUSAKA, and HIROSHI KAWAKAMI. "BIFURCATION AND CHAOS IN COUPLED BVP OSCILLATORS." International Journal of Bifurcation and Chaos 14, no. 04 (April 2004): 1305–24. http://dx.doi.org/10.1142/s0218127404009983.
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Bonhöffer–van der Pol(BVP) oscillator is a classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region, create the double scroll attractor due to the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in the experimental laboratory.
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Kabana, Sonia, and Peter Minkowski. "Counting of oscillatory modes of valence quarks forming q–q̄ mesons." International Journal of Modern Physics A 31, no. 07 (March 2, 2016): 1650023. http://dx.doi.org/10.1142/s0217751x16500238.
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We present the unique properties of oscillatory modes of valence quarks [Formula: see text] and antiquarks in mesons and the mass spectrum of associated mesons. The mesonic multiplets are shown to emerge from the picture of oscillating quarks and antiquarks in three space dimensions in the center of mass system of the mesons. All oscillatory modes are fully relativistic with a finite number of oscillators and this is forming the unique harmonic oscillator with these properties. The density of states as a function of masssquare is calculated. Since it is known that there are missing states of unobserved hadrons this estimate is of relevance for the accounting of the latter, as the here estimated mesonic multiplets include both the observed and the unobserved (or “missing”) hadrons. The estimate is conceptually different from Hagedorn’s model and is based on field theory of QCD.
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Yeremieiev, Volodymyr, Oleksandr Briantsev, Oleksii Naumuk, and Volodymyr Samoilov. "Software for research oscillation process in the system of oscillators with different masses." Ukrainian Journal of Educational Studies and Information Technology 7, no. 4 (December 30, 2019): 10–23. http://dx.doi.org/10.32919/uesit.2019.04.02.
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A mathematical model is formulated as a system of differential equations for the analysis of the oscillatory process in a linear oscillators with different masses. It is assumed that the left end of the first oscillator is fixed and an arbitrary force is attached to the last oscillator. Proposed an algorithm for solving the problem using the numerical methods Euler and Runga-Kutt. Two Euler and RungK applications have been developed for calculations. The program code is compiled in C++ algorithmic language in Microsoft Visual Studio 2012. The accuracy of the calculated data depends on the number of oscillators and the time of oscillation. Testing showed that in the case of one or two oscillators, the program RungK, based on the Rung-Kutta method, provides 10-10% accuracy of calculations. The error of the calculated parameters is almost independent of the number of time intervals from 103 to 106. The accuracy of the Euler method, which is implemented in Euler, is about 0.5% under similar conditions. Increasing the number of iterations to 104, 105, and 106 leads to an increase in accuracy to 0.05%, 0.005%, and 0.0005%, respectively. The program can be useful in the analysis of oscillatory processes in a linear oscillate ditch.
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Kabana, Sonia, and Peter Minkowski. "Counting of oscillatory modes of valence quarks forming qqq baryons for three quark flavors u, d, s." International Journal of Modern Physics A 32, no. 04 (February 9, 2017): 1750004. http://dx.doi.org/10.1142/s0217751x1750004x.
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We present the unique properties of oscillatory modes of [Formula: see text] light quarks — [Formula: see text], [Formula: see text], [Formula: see text] — using the [Formula: see text] broken symmetry classification. [Formula: see text] stands for the space rotation group generated by the sum of the three individual angular momenta of quarks in their c.m. system. The baryonic multiplets are shown to emerge from the picture of oscillating quarks in three space dimensions in the center-of-mass system of the baryons. All oscillatory modes are fully relativistic with a finite number of oscillators and this is forming the unique harmonic oscillator with these properties. The density of states as a function of mass-square is calculated. This estimate is of relevance for the accounting of the missing states of unobserved hadrons, as the here estimated baryonic multiplets include both the observed and the unobserved (or “missing”) hadrons. The estimate is conceptually different from Hagedorn’s model and is based on field theory of QCD.
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Jezzini, Sami H., Andrew A. V. Hill, Pavlo Kuzyk, and Ronald L. Calabrese. "Detailed Model of Intersegmental Coordination in the Timing Network of the Leech Heartbeat Central Pattern Generator." Journal of Neurophysiology 91, no. 2 (February 2004): 958–77. http://dx.doi.org/10.1152/jn.00656.2003.
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To address the general problem of intersegmental coordination of oscillatory neuronal networks, we have studied the leech heartbeat central pattern generator. The core of this pattern generator is a timing network that consists of two segmental oscillators, each of which comprises two identified, reciprocally inhibitory oscillator interneurons. Intersegmental coordination between the segmental oscillators is mediated by synaptic interactions between the oscillator interneurons and identified coordinating interneurons. The small number of neurons (8) and the distributed structure of the timing network have made the experimental analysis of the segmental oscillators as discrete, independent units possible. On the basis of this experimental work, we have made conductance-based models to explore how intersegmental phase and cycle period are determined. We show that although a previous simple model, which ignored many details of the living system, replicated some essential features of the living system, the incorporation of specific cellular and network properties is necessary to capture the behavior of the system seen under different experimental conditions. For example, spike frequency adaptation in the coordinating interneurons and details of asymmetries in intersegmental connectivity are necessary for replicating driving experiments in which one segmental oscillator was injected with periodic current pulses to entrain the activity of the entire network. Nevertheless, the basic mechanisms of phase and period control demonstrated here appear to be very general and could be used by other networks that produce coordinated segmental motor outflow.
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Kurkin, Semen A., Danil D. Kulminskiy, Vladimir I. Ponomarenko, Mikhail D. Prokhorov, Sergey V. Astakhov, and Alexander E. Hramov. "Central pattern generator based on self-sustained oscillator coupled to a chain of oscillatory circuits." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 3 (March 2022): 033117. http://dx.doi.org/10.1063/5.0077789.
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We have proposed and studied both numerically and experimentally a multistable system based on a self-sustained Van der Pol oscillator coupled to passive oscillatory circuits. The number of passive oscillators determines the number of multistable oscillatory regimes coexisting in the proposed system. It is shown that our system can be used in robotics applications as a simple model for a central pattern generator (CPG). In this case, the amplitude and phase relations between the active and passive oscillators control a gait, which can be adjusted by changing the system control parameters. Variation of the active oscillator’s natural frequency leads to hard switching between the regimes characterized by different phase shifts between the oscillators. In contrast, the external forcing can change the frequency and amplitudes of oscillations, preserving the phase shifts. Therefore, the frequency of the external signal can serve as a control parameter of the model regime and realize a feedback in the proposed CPG depending on the environmental conditions. In particular, it allows one to switch the regime and change the velocity of the robot’s gate and tune the gait to the environment. We have also shown that the studied oscillatory regimes in the proposed system are robust and not affected by external noise or fluctuations of the system parameters. Moreover, using the proposed scheme, we simulated the type of bipedal locomotion, including walking and running.
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Wang, Chunzai. "A review of ENSO theories." National Science Review 5, no. 6 (October 10, 2018): 813–25. http://dx.doi.org/10.1093/nsr/nwy104.
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Abstract The El Niño and the Southern Oscillation (ENSO) occurrence can be usually explained by two views of (i) a self-sustained oscillatory mode and (ii) a stable mode interacting with high-frequency forcing such as westerly wind bursts and Madden-Julian Oscillation events. The positive ocean–atmosphere feedback in the tropical Pacific hypothesized by Bjerknes leads the ENSO event to a mature phase. After ENSO event matures, negative feedbacks are needed to cease the ENSO anomaly growth. Four negative feedbacks have been proposed: (i) reflected Kelvin waves at the ocean western boundary, (ii) a discharge process due to Sverdrup transport, (iii) western-Pacific wind-forced Kelvin waves and (iv) anomalous zonal advections and wave reflection at the ocean eastern boundary. These four ENSO mechanisms are respectively called the delayed oscillator, the recharge–discharge oscillator, the western-Pacific oscillator and the advective–reflective oscillator. The unified oscillator is developed by including all ENSO mechanisms, i.e. all four ENSO oscillators are special cases of the unified oscillator. The tropical Pacific Ocean and atmosphere interaction can also induce coupled slow westward- and eastward-propagating modes. An advantage of the coupled slow modes is that they can be used to explain the propagating property of interannual anomalies, whereas the oscillatory modes produce a standing oscillation. The research community has recently paid attention to different types of ENSO events by focusing on the central-Pacific El Niño. All of the ENSO mechanisms may work for the central-Pacific El Niño events, with an addition that the central-Pacific El Niño may be related to forcing or processes in the extra-tropical Pacific.
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Chen, Meng, Dan Meng, Heng Jiang, and Yuren Wang. "Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial." Shock and Vibration 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/1369858.
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The acoustic characteristics of 2D single-oscillator, dual-oscillator, and triple-oscillator acoustic metamaterials were investigated based on concentric ring structures using the finite element method. For the single-oscillator, dual-oscillator, and triple-oscillator models investigated here, the dipolar resonances of the scatterer always induce negative effective mass density, preventing waves from propagating in the structure, thus forming the band gap. As the number of oscillators increases, relative movements between the oscillators generate coupling effect; this increases the number of dipolar resonance modes, causes negative effective mass density in more frequency ranges, and increases the number of band gaps. It can be seen that the number of oscillators in the cell is closely related to the number of band gaps due to the coupling effect, when the filling rate is of a certain value.
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BONNIN, MICHELE, FERNANDO CORINTO, and MARCO GILLI. "BIFURCATIONS, STABILITY AND SYNCHRONIZATION IN DELAYED OSCILLATORY NETWORKS." International Journal of Bifurcation and Chaos 17, no. 11 (November 2007): 4033–48. http://dx.doi.org/10.1142/s0218127407019846.
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Current studies in neurophysiology award a key role to collective behaviors in both neural information and image processing. This fact suggests to exploit phase locking and frequency entrainment in oscillatory neural networks for computational purposes. In the practical implementation of artificial neural networks delays are always present due to the non-null processing time and the finite signal propagation speed. This manuscript deals with networks composed by delayed oscillators, we show that either long delays or constant external inputs can elicit oscillatory behavior in the single neural oscillator. Using center manifold reduction and normal form theory, the equations governing the whole network dynamics are reduced to an amplitude-phase model (i.e. equations describing the evolution of both the amplitudes and the phases of the oscillators). The analysis of a network with a simple architecture reveals that different kind of phase locked oscillations are admissible, and the possible coexistence of in-phase and anti-phase locked solutions.
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Matsuda, Takeru, Fumitaka Homae, Hama Watanabe, Gentaro Taga, and Fumiyasu Komaki. "Oscillator decomposition of infant fNIRS data." PLOS Computational Biology 18, no. 3 (March 24, 2022): e1009985. http://dx.doi.org/10.1371/journal.pcbi.1009985.
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The functional near-infrared spectroscopy (fNIRS) can detect hemodynamic responses in the brain and the data consist of bivariate time series of oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) on each channel. In this study, we investigate oscillatory changes in infant fNIRS signals by using the oscillator decompisition method (OSC-DECOMP), which is a statistical method for extracting oscillators from time series data based on Gaussian linear state space models. OSC-DECOMP provides a natural decomposition of fNIRS data into oscillation components in a data-driven manner and does not require the arbitrary selection of band-pass filters. We analyzed 18-ch fNIRS data (3 minutes) acquired from 21 sleeping 3-month-old infants. Five to seven oscillators were extracted on most channels, and their frequency distribution had three peaks in the vicinity of 0.01-0.1 Hz, 1.6-2.4 Hz and 3.6-4.4 Hz. The first peak was considered to reflect hemodynamic changes in response to the brain activity, and the phase difference between oxy-Hb and deoxy-Hb for the associated oscillators was at approximately 230 degrees. The second peak was attributed to cardiac pulse waves and mirroring noise. Although these oscillators have close frequencies, OSC-DECOMP can separate them through estimating their different projection patterns on oxy-Hb and deoxy-Hb. The third peak was regarded as the harmonic of the second peak. By comparing the Akaike Information Criterion (AIC) of two state space models, we determined that the time series of oxy-Hb and deoxy-Hb on each channel originate from common oscillatory activity. We also utilized the result of OSC-DECOMP to investigate the frequency-specific functional connectivity. Whereas the brain oscillator exhibited functional connectivity, the pulse waves and mirroring noise oscillators showed spatially homogeneous and independent changes. OSC-DECOMP is a promising tool for data-driven extraction of oscillation components from biological time series data.
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KAWANARI, TOSHIHIRO, and SEIICHIRO MORO. "MULTI-PHASE OSCILLATION IN RF CMOS LC OSCILLATORS COUPLED BY MUTUAL INDUCTORS." Journal of Circuits, Systems and Computers 19, no. 04 (June 2010): 733–47. http://dx.doi.org/10.1142/s0218126610006402.
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When the oscillators are coupled, coupling methods are very important and influence some factors, for example, increasing or decreasing of noise and whether multi-phase synchronization phenomena can be observed or not due to the number of oscillators and so on. In this paper, multi-phase synchronization phenomena which are generated in RF CMOS LC oscillators with mutual inductor couplings and the stability of various oscillatory modes in the proposed model are investigated. In the proposed system, multi-phase synchronization phenomena can be observed regardless of the number of oscillators in RF region due to setting up the sign of the mutual inductance properly, and the each oscillatory mode is stable.
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Velichko, Andrei, Maksim Belyaev, and Petr Boriskov. "A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing." Electronics 8, no. 1 (January 9, 2019): 75. http://dx.doi.org/10.3390/electronics8010075.
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The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 × 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.
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STÉPÁN, GÁBOR, TAMÁS INSPERGER, and RÓBERT SZALAI. "DELAY, PARAMETRIC EXCITATION, AND THE NONLINEAR DYNAMICS OF CUTTING PROCESSES." International Journal of Bifurcation and Chaos 15, no. 09 (September 2005): 2783–98. http://dx.doi.org/10.1142/s0218127405013642.
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It is a rule of thumb that time delay tends to destabilize any dynamical system. This is not true, however, in the case of delayed oscillators, which serve as mechanical models for several surprising physical phenomena. Parametric excitation of oscillatory systems also exhibits stability properties sometimes defying our physical sense. The combination of the two effects leads to challenging tasks when nonlinear dynamic behaviors in these systems are to be predicted or explained as well. This paper gives a brief historical review of the development of stability analysis in these systems, induced by newer and newer models in several fields of engineering. Local and global nonlinear behavior is also discussed in the case of the most typical parametrically excited delayed oscillator, a recent model of cutting applied to the study of high-speed milling processes.
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CORINTO, FERNANDO, MICHELE BONNIN, and MARCO GILLI. "WEAKLY CONNECTED OSCILLATORY NETWORK MODELS FOR ASSOCIATIVE AND DYNAMIC MEMORIES." International Journal of Bifurcation and Chaos 17, no. 12 (December 2007): 4365–79. http://dx.doi.org/10.1142/s0218127407020014.
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Several studies in neuroscience have shown that nonlinear oscillatory networks represent bio-inspired models for information and image processing. Recent studies on the thalamo-cortical system have shown that weakly connected oscillatory networks (WCONs) exhibit associative properties and can be exploited for dynamic pattern recognition. In this manuscript we focus on WCONs, composed of oscillators that adhere to a Lur'e like description and are organized in such a way that they communicate one another, through a common medium. The main dynamic features are investigated by exploiting the phase deviation equation (i.e. the equation that describes the phase variation of each oscillator, due to weak coupling). Firstly a very accurate analytic expression of the phase deviation equation is derived, by jointly describing the function technique and the Malkin's Theorem. Furthermore, by using a simple learning algorithm, the phase-deviation equation is designed in such a way that given sets of patterns can be stored and recalled. In particular, two models of WCONs are presented as examples of associative and dynamic memories.
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Hill, Andrew A. V., Mark A. Masino, and Ronald L. Calabrese. "Model of Intersegmental Coordination in the Leech Heartbeat Neuronal Network." Journal of Neurophysiology 87, no. 3 (March 1, 2002): 1586–602. http://dx.doi.org/10.1152/jn.00337.2001.
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We have created a computational model of the timing network that paces the heartbeat of the medicinal leech, Hirudo medicinalis. The rhythmic activity of this network originates from two segmental oscillators located in the third and fourth midbody ganglia. In the intact nerve cord, these segmental oscillators are mutually entrained to the same cycle period. Although experiments have shown that the segmental oscillators are coupled by inhibitory coordinating interneurons, the underlying mechanisms of intersegmental coordination have not yet been elucidated. To help understand this coordination, we have created a simple computational model with two variants: symmetric and asymmetric. In the symmetric model, neurons within each segmental oscillator called oscillator interneurons, inhibit the coordinating interneurons. In contrast, in the asymmetric model only the oscillator interneurons of one segmental oscillator inhibit the coordinating interneurons. In the symmetric model, when two segmental oscillators with different inherent periods are coupled, the faster one leads in phase, and the period of the coupled system is equal to the period of the faster oscillator. This behavior arises because, during each oscillation cycle, the oscillator interneurons of the faster segmental oscillator begin to burst before those of the slower oscillator, thereby terminating spike activity in the coordinating interneurons. Thus there is a brief period of time in each cycle when the oscillator interneurons of the slower segmental oscillator are relieved of inhibition from the coordinating interneurons. This “removal of synaptic inhibition” allows, within certain limits, the slower segmental oscillator to be sped to the period of the faster one. Thus the symmetric model demonstrates a plausible biophysical mechanism by which one segmental oscillator can entrain the other. In general the asymmetric model, in which only one segmental oscillator has the ability to inhibit the coordinating interneurons, behaves similarly, except only one segmental oscillator can control the period of the system. In addition, we simulated physiological experiments in which a “driving” stimulus, consisting of alternating positive and negative current steps, was used to control a single oscillator interneuron and thereby entrain the activity of the entire timing network.
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FUJISAKA, HIROKAZU, NAOFUMI TSUKAMOTO, and SATOKI UCHIYAMA. "CHAOTIC PHASE SYNCHRONIZATION AND ITS BREAKDOWN - MAPPING MODEL AND CRITICAL DYNAMICS." International Journal of Modern Physics B 21, no. 23n24 (September 30, 2007): 3909–17. http://dx.doi.org/10.1142/s0217979207044950.
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In the present paper, we briefly discuss the construction of mapping model of coupled oscillator systems for limit-cycle oscillators and chaotic oscillators. A comparison of the proposed mapping model and other models, i.e., the Ikeda map and the phase map model is made. Furthermore, the critical dynamics associated with the breakdown of chaotic phase synchronization based on the present mapping model is discussed.
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Zaitsev, Valery V., and Alexander V. Karlov. "Quasi-harmonic self-oscillations in discrete time: analysis and synthesis of dynamic systems." Physics of Wave Processes and Radio Systems 24, no. 4 (January 16, 2022): 19–24. http://dx.doi.org/10.18469/1810-3189.2021.24.4.19-24.
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For sampling of time in a differential equation of movement of Thomson type oscillator (generator) it is offered to use a combination of the numerical method of finite differences and an asymptotic method of the slowl-changing amplitudes. The difference approximations of temporal derivatives are selected so that, first, to save conservatism and natural frequency of the linear circuit of self-oscillatory system in the discrete time. Secondly, coincidence of the difference shortened equation for the complex amplitude of self-oscillations in the discrete time with Eulers approximation of the shortened equation for amplitude of self-oscillations in analog system prototype is required. It is shown that realization of such approach allows to create discrete mapping of the van der Pol oscillator and a number of mappings of Thomson type oscillators. The adequacy of discrete models to analog prototypes is confirmed with also numerical experiment.
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Boujo, E., and N. Noiray. "Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160894. http://dx.doi.org/10.1098/rspa.2016.0894.
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We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator’s damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker–Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations—for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker–Planck equation is solved to compute Kramers–Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
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Ghose, Geoffrey M., and Ralph D. Freeman. "Intracortical connections are not required for oscillatory activity in the visual cortex." Visual Neuroscience 14, no. 6 (November 1997): 963R—979R. http://dx.doi.org/10.1017/s0952523800011901.
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Abstractarises from the integration of signals from strongly oscillatory cells within the LGN. The model also predicts the incidence of 50-Hz oscillatory cells within the cortex. Oscillatory discharge around 30 Hz is explained in a second model by the presence of intrinsically oscillatory cells within cortical layer 5. Both models generate spike trains whose power spectra and mean firing rates are in close agreement with experimental observations of simple and complex cells. Considered together, the two models can largely account for the nature and incidence of oscillatory discharge in the cat's visual cortex. The validity of these models is consistent with the possibility that oscillations are generated independently of intracortical interactions. Because these models rely on intrinsic stimulus-independent oscillators within the retina and cortex, the results further suggest that oscillatory activity within the cortex is not necessarily associated with the processing of high-order visual information.
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Doelling, Keith B., M. Florencia Assaneo, Dana Bevilacqua, Bijan Pesaran, and David Poeppel. "An oscillator model better predicts cortical entrainment to music." Proceedings of the National Academy of Sciences 116, no. 20 (April 24, 2019): 10113–21. http://dx.doi.org/10.1073/pnas.1816414116.
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A body of research demonstrates convincingly a role for synchronization of auditory cortex to rhythmic structure in sounds including speech and music. Some studies hypothesize that an oscillator in auditory cortex could underlie important temporal processes such as segmentation and prediction. An important critique of these findings raises the plausible concern that what is measured is perhaps not an oscillator but is instead a sequence of evoked responses. The two distinct mechanisms could look very similar in the case of rhythmic input, but an oscillator might better provide the computational roles mentioned above (i.e., segmentation and prediction). We advance an approach to adjudicate between the two models: analyzing the phase lag between stimulus and neural signal across different stimulation rates. We ran numerical simulations of evoked and oscillatory computational models, showing that in the evoked case,phase lag is heavily rate-dependent, while the oscillatory model displays marked phase concentration across stimulation rates. Next, we compared these model predictions with magnetoencephalography data recorded while participants listened to music of varying note rates. Our results show that the phase concentration of the experimental data is more in line with the oscillatory model than with the evoked model. This finding supports an auditory cortical signal that (i) contains components of both bottom-up evoked responses and internal oscillatory synchronization whose strengths are weighted by their appropriateness for particular stimulus types and (ii) cannot be explained by evoked responses alone.
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Bonnin, Michele. "Phase oscillator model for noisy oscillators." European Physical Journal Special Topics 226, no. 15 (December 2017): 3227–37. http://dx.doi.org/10.1140/epjst/e2016-60319-0.
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Wang, Wei-Ping. "Binary-Oscillator Networks: Bridging a Gap between Experimental and Abstract Modeling of Neural Networks." Neural Computation 8, no. 2 (February 15, 1996): 319–39. http://dx.doi.org/10.1162/neco.1996.8.2.319.
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This paper proposes a simplified oscillator model, called binary-oscillator, and develops a class of neural network models having binary-oscillators as basic units. The binary-oscillator has a binary dynamic variable v = ±1 modeling the “membrane potential” of a neuron, and due to the presence of a “slow current” (as in a classical relaxation-oscillator) it can oscillate between two states. The purpose of the simplification is to enable abstract algorithmic study on the dynamics of oscillator networks. A binary-oscillator network is formally analogous to a system of stochastic binary spins (atomic magnets) in statistical mechanics.
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GAVRILIK, A. M., and A. P. REBESH. "PLETHORA OF q-OSCILLATORS POSSESSING PAIRWISE ENERGY LEVEL DEGENERACY." Modern Physics Letters A 23, no. 13 (April 30, 2008): 921–32. http://dx.doi.org/10.1142/s021773230802687x.
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Using the q, p-deformed oscillators as basic generating system, we obtain diverse classes (which form distinct sectors of functional continua) of novel versions of q-deformed oscillators, all of which share the property of "accidental" degeneracy within a fixed pair of energy levels Em = Em+1, m ≥ 1, occurring at the real deformation parameter fixed by an appropriate value q(m) that depends on m and on particular model. Likewise, the degeneracy E0 = Ek (where k ≥ 2) takes place, for properly fixed q = q(k), in most of those models. The formerly studied model of q-oscillator known as the Tamm–Dancoff cutoff deformed oscillator is contained in the continua as isolated special case.
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RUWISCH, DIETMAR, MATHIAS BODE, DENIS VOLKOV, and EVGENII VOLKOV. "COLLECTIVE MODES OF THREE COUPLED RELAXATION OSCILLATORS: THE INFLUENCE OF DETUNING." International Journal of Bifurcation and Chaos 09, no. 10 (October 1999): 1969–81. http://dx.doi.org/10.1142/s0218127499001437.
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The dynamics of a ring of three relaxation oscillators symmetrically coupled in the slow variable is considered both experimentally and by means of numerical simulations. It is shown that apart from the synchronous oscillation the basic set of periodic attractors typical for identical oscillators is not essentially affected by a small detuning. However, detuning creates a large set of new collective modes which are characterized by larger system periods and a variety of phase relations between the oscillators. Comparisons of the experimental data with different oscillator models reveal that the results do not crucially depend on the specific features of the models and possible experimental uncertainties.
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Smelov, Pavel S., Ivan S. Proskurkin, and Vladimir K. Vanag. "Controllable switching between stable modes in a small network of pulse-coupled chemical oscillators." Physical Chemistry Chemical Physics 21, no. 6 (2019): 3033–43. http://dx.doi.org/10.1039/c8cp07374k.
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Laszuk, Dawid, Jose O. Cadenas, and Slawomir J. Nasuto. "KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem." Advances in Data Science and Adaptive Analysis 10, no. 02 (April 2018): 1840002. http://dx.doi.org/10.1142/s2424922x18400028.
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Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals.
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Ruks, Lewis, and Robert A. Van Gorder. "On the Inverse Problem of Competitive Modes and the Search for Chaotic Dynamics." International Journal of Bifurcation and Chaos 27, no. 10 (September 2017): 1730032. http://dx.doi.org/10.1142/s0218127417300324.
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Generalized competitive modes (GCM) have been used as a diagnostic tool in order to analytically identify parameter regimes which may lead to chaotic trajectories in a given first order nonlinear dynamical system. The approach involves recasting the first order system as a second order nonlinear oscillator system, and then checking to see if certain conditions on the modes of these oscillators are satisfied. In the present paper, we will consider the inverse problem of GCM: If a system of second order oscillator equations satisfy the GCM conditions, can we then construct a first order dynamical system from it which admits chaotic trajectories? Solving the direct inverse problem is equivalent to finding solutions to an inhomogeneous form of the Euler equations. As there are no general solutions to this PDE system, we instead consider the problem for restricted classes of functions for autonomous systems which, upon obtaining the nonlinear oscillatory representation, we are able to extract at least two of the modes explicitly. We find that these methods often make finding chaotic regimes a much simpler task; many classes of parameter-function regimes that lead to nonchaos are excluded by the competitive mode conditions, and classical knowledge of dynamical systems then allows us to tune the free parameters or functions appropriately in order to obtain chaos. To find new hyperchaotic systems, a similar approach is used, but more effort and additional considerations are needed. These results demonstrate one method for constructing new chaotic or hyperchaotic systems.
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Chorti, Arsenia. "How to Model the Near-to-the-Carrier Regime and the Lower Knee Frequency of Real RF Oscillators." Journal of Electrical and Computer Engineering 2010 (2010): 1–4. http://dx.doi.org/10.1155/2010/537132.
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Numerous empirical data demonstrate that real noisy RF oscillators are affected by power-law phase noise. However, until recently, the robust analytic modeling of the deep-into-the-carrier spectral regime of RF oscillators was intangible due to the infinities involved in the relevant power-law regions. In this letter we demonstrate how recent advances in oscillator spectral modeling can be applied to extrapolate the near-to-the-carrier regime as well as estimate the oscillator lower knee frequency of transition between the deep-into-the-carrier regime and the power-law regions of real RF oscillators.
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Wang, Tianmiao, Yonghui Hu, and Jianhong Liang. "Learning to swim: a dynamical systems approach to mimicking fish swimming with CPG." Robotica 31, no. 3 (July 18, 2012): 361–69. http://dx.doi.org/10.1017/s0263574712000343.
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SUMMARYCentral Pattern Generators (CPGs) can generate robust, smooth and coordinated oscillatory signals for locomotion control of robots with multiple degrees of freedom, but the tuning of CPG parameters for a desired locomotor pattern constitutes a tremendously difficult task. This paper addresses this problem for the generation of fish-like swimming gaits with an adaptive CPG network on a multi-joint robotic fish. Our approach converts the related CPG parameters into dynamical systems that evolve as part of the CPG network dynamics. To reproduce the bodily motion of swimming fish, we use the joint angles calculated with the trajectory approximation method as teaching signals for the CPG network, which are modeled as a chain of coupled Hopf oscillators. A novel coupling scheme is proposed to eliminate the influence of afferent signals on the amplitude of the oscillator. The learning rules of intrinsic frequency, coupling weight and amplitude are formulated with phase space representation of the oscillators. The frequency, amplitudes and phase relations of the teaching signals can be encoded by the CPG network with adaptation mechanisms. Since the Hopf oscillator exhibits limit cycle behavior, the learned locomotor pattern is stable against perturbations. Moreover, due to nonlinear characteristics of the CPG model, modification of the target travelling body wave can be carried out in a smooth way. Numerical experiments are conducted to validate the effectiveness of the proposed learning rules.
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Radovancevic, Darko, and Ljubisa Nesic. "Kantowski-Sachs minisuperspace cosmological model on noncommutative space." Facta universitatis - series: Physics, Chemistry and Technology 14, no. 1 (2016): 21–26. http://dx.doi.org/10.2298/fupct1601021r.
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A vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model is considered. In a classical case, Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model is formulated also on noncommutative space.
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Horn, David, and Irit Opher. "Temporal Segmentation in a Neural Dynamic System." Neural Computation 8, no. 2 (February 15, 1996): 373–89. http://dx.doi.org/10.1162/neco.1996.8.2.373.
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Oscillatory attractor neural networks can perform temporal segmentation, i.e., separate the joint inputs they receive, through the formation of staggered oscillations. This property, which may be basic to many perceptual functions, is investigated here in the context of a symmetric dynamic system. The fully segmented mode is one type of limit cycle that this system can develop. It can be sustained for only a limited number n of oscillators. This limitation to a small number of segments is a basic phenomenon in such systems. Within our model we can explain it in terms of the limited range of narrow subharmonic solutions of the single nonlinear oscillator. Moreover, this point of view allows us to understand the dominance of three leading amplitudes in solutions of partial segmentation, which are obtained for high n. The latter are also abundant when we replace the common input with a graded one, allowing for different inputs to different oscillators. Switching to an input with fluctuating components, we obtain segmentation dominance for small systems and quite irregular waveforms for large systems.
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Ghose, Geoffrey M., and Ralph D. Freeman. "Intracortical connections are not required for oscillatory activity in the visual cortex." Visual Neuroscience 14, no. 5 (September 1997): 963–79. http://dx.doi.org/10.1017/s0952523800011676.
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AbstractSynchronized oscillatory discharge in the visual cortex has been proposed to underlie the linking of retinotopically disparate features into perceptually coherent objects. These proposals have largely relied on the premise that the oscillations arise from intracortical circuitry. However, strong oscillations within both the retina and the lateral geniculate nucleus (LGN) have been reported recently. To evaluate the possibility that cortical oscillations arise from peripheral pathways, we have developed two plausible models of single cell oscillatory discharge that specifically exclude intracortical networks. In the first model, cortical oscillatory discharge near 50 Hz in frequency arises from the integration of signals from strongly oscillatory cells within the LGN. The model also predicts the incidence of 50-Hz oscillatory cells within the cortex. Oscillatory discharge around 30 Hz is explained in a second model by the presence of intrinsically oscillatory cells within cortical layer 5. Both models generate spike trains whose power spectra and mean firing rates are in close agreement with experimental observations of simple and complex cells. Considered together, the two models can largely account for the nature and incidence of oscillatory discharge in the cat's visual cortex. The validity of these models is consistent with the possibility that oscillations are generated independently of intracortical interactions. Because these models rely on intrinsic stimulus-independent oscillators within the retina and cortex, the results further suggest that oscillatory activity within the cortex is not necessarily associated with the processing of high-order visual information.
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Hattori, Yuya, Michiyo Suzuki, Zu Soh, Yasuhiko Kobayashi, and Toshio Tsuji. "Theoretical and Evolutionary Parameter Tuning of Neural Oscillators with a Double-Chain Structure for Generating Rhythmic Signals." Neural Computation 24, no. 3 (March 2012): 635–75. http://dx.doi.org/10.1162/neco_a_00249.
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A neural oscillator with a double-chain structure is one of the central pattern generator models used to simulate and understand rhythmic movements in living organisms. However, it is difficult to reproduce desired rhythmic signals by tuning an enormous number of parameters of neural oscillators. In this study, we propose an automatic tuning method consisting of two parts. The first involves tuning rules for both the time constants and the amplitude of the oscillatory outputs based on theoretical analyses of the relationship between parameters and outputs of the neural oscillators. The second involves an evolutionary tuning method with a two-step genetic algorithm (GA), consisting of a global GA and a local GA, for tuning parameters such as neural connection weights that have no exact tuning rule. Using numerical experiments, we confirmed that the proposed tuning method could successfully tune all parameters and generate sinusoidal waves. The tuning performance of the proposed method was less affected by factors such as the number of excitatory oscillators or the desired outputs. Furthermore, the proposed method was applied to the parameter-tuning problem of some types of artificial and biological wave reproduction and yielded optimal parameter values that generated complex rhythmic signals in Caenorhabditis elegans without trial and error.
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Karpenko, V. M., Yu P. Starodub, and O. V. Karpenko. "GEODYNAMICS." GEODYNAMICS 1(6)2007, no. 1(6) (September 20, 2007): 81–84. http://dx.doi.org/10.23939/jgd2007.01.081.
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The questions, related to the informative features of oscillator dynamics, which succeed to be learned with the use of energy-informatics approach, are examined in this article. The spatial and kinematics parameters of simple oscillator are examined depending on energy that gives the possibility to define the dynamic parameters of oscillator - mass and rigidity. Oscillators are explored with the use of energy-informatics approach with the solution of inverse problem - the determination of mass and flexibility of oscillators' vibrations, which as separate chain lets model the medium.
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Pfirsch, D. "Nonlinear Instabilities, Negative Energy Modes and Generalized Cherry Oscillators." Zeitschrift für Naturforschung A 45, no. 7 (July 1, 1990): 839–46. http://dx.doi.org/10.1515/zna-1990-0701.
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AbstractIn 1925 Cherry [1] discussed two oscillators of positive and negative energy that are nonlinearly coupled in a special way, and presented a class of exact solutions of the nonlinear equations showing explosive instability independent of the strength of the nonlinearity and the initial amplitudes. In this paper Cherry's Hamiltonian is transformed into a form which allows a simple physical interpretation. The new Hamiltonian is generalized to three nonlinearly coupled oscillators; it corresponds to three-wave interaction in a continuum theory, like the Vlasov-Maxwell theory, if there exist linear negative energy waves [2-4, 5, 6], Cherry was able to present a two-parameter solution set for his example which would, however, allow a four-parameter solution set, and, as a first result, an analogous three-parameter solution set for the resonant three-oscillator case is obtained here which, however, would allow a six-parameter solution set. Nonlinear instability is therefore proven so far only for a very small part of the phase space of the oscillators. This paper gives in addition the complete solution for the three-oscillator case and shows that, except for a singular case, all initial conditions, especially those with arbitrarily small amplitudes, lead to explosive behaviour. This is true of the resonant case. The non-resonant oscillators can sometimes also become explosively unstable, but the initial amplitudes must not be infinitesimally small. A few examples are presented for illustration.
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Zhang, Honghui, and Pengcheng Xiao. "Seizure Dynamics of Coupled Oscillators with Epileptor Field Model." International Journal of Bifurcation and Chaos 28, no. 03 (March 2018): 1850041. http://dx.doi.org/10.1142/s0218127418500414.
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The focus of this paper is to investigate the dynamics of seizure activities by using the Epileptor coupled model. Based on the coexistence of seizure-like event (SLE), refractory status epilepticus (RSE), depolarization block (DB), and normal state, we first study the dynamical behaviors of two coupled oscillators in different activity states with Epileptor model by linking them with slow permittivity coupling. Our research has found that when one oscillator in normal states is coupled with any oscillator in SLE, RSE or DB states, these two oscillators can both evolve into SLE states under appropriate coupling strength. And then these two SLE oscillators can perform epileptiform synchronization or epileptiform anti-synchronization. Meanwhile, SLE can be depressed when considering the fast electrical or chemical coupling in Epileptor model. Additionally, a two-dimensional reduced model is also given to show the effect of coupling number on seizures. Those results can help to understand the dynamical mechanism of the initiation, maintenance, propagation and termination of seizures in focal epilepsy.
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Morgan, Louis W., Jerry F. Feldman, and Deborah Bell-Pedersen. "Genetic interactions between clock mutations in Neurospora crassa : can they help us to understand complexity?" Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 356, no. 1415 (November 29, 2001): 1717–24. http://dx.doi.org/10.1098/rstb.2001.0967.
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Recent work on circadian clocks in Neurospora has primarily focused on the frequency ( frq ) and white–collar ( wc ) loci. However, a number of other genes are known that affect either the period or temperature compensation of the rhythm. These include the period (no relationship to the period gene of Drosophila ) genes and a number of genes that affect cellular metabolism. How these other loci fit into the circadian system is not known, and metabolic effects on the clock are typically not considered in single–oscillator models. Recent evidence has pointed to multiple oscillators in Neurospora , at least one of which is predicted to incorporate metabolic processes. Here, the Neurospora clock–affecting mutations will be reviewed and their genetic interactions discussed in the context of a more complex clock model involving two coupled oscillators: a FRQ/WC–based oscillator and a ‘ frq –less’ oscillator that may involve metabolic components.
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Li, Yang, Jifan Shi, and Kazuyuki Aihara. "Mean-field analysis of Stuart–Landau oscillator networks with symmetric coupling and dynamical noise." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063114. http://dx.doi.org/10.1063/5.0081295.
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This paper presents analyses of networks composed of homogeneous Stuart–Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.
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Fu, Yongqing, Yanan Li, Lin Zhang, and Xingyuan Li. "The DPSK Signal Noncoherent Demodulation Receiver Based on the Duffing Oscillators Array." International Journal of Bifurcation and Chaos 26, no. 13 (December 15, 2016): 1650216. http://dx.doi.org/10.1142/s0218127416502163.
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Chaotic communication requires the knowledge of corresponding phase relationship between the primary phase of Duffing oscillator’s internal driving force and the primary phase of the undetected signal. Currently, there is no method of noncoherent demodulation for DPSK (Differential Phase Shift Keying) signal and mobile communication signal by Duffing oscillator. To solve this problem, this study presents a noncoherent demodulation method based on the Duffing oscillators array and Duffing oscillator optimization. We first present the model of Duffing oscillator and its sensitivity to undetected signal primary phase. Then the zone partition is proposed to identify the Duffing oscillator’s phase trajectory, and subsequently, the mathematical model and implementation method of the Duffing oscillators array are outlined. Thirdly, the Duffing oscillator optimization and its adaptive strobe technique are proposed, also their application to DPSK signal noncoherent demodulation are discussed. Finally, the design of new concept DPSK chaotic digital receiver based on the Duffing oscillators array is presented, together with its simulation results obtained by using SystemView simulation platform. The simulation results suggest that the new concept receiver based on the Duffing oscillator optimization of Duffing oscillators array owns better SNR (signal-to-noise ratio) threshold property than typical existing receivers (chaotic or nonchaotic) in the AWGN (additive white Gaussian noise) channel and multipath Rayleigh fading channel. In addition, the new concept receiver may detect mobile communication signal.
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ITOH, MAKOTO, and LEON O. CHUA. "NONLINEAR OSCILLATORS WITH HYSTERETIC CHUA'S DIODES." International Journal of Bifurcation and Chaos 15, no. 05 (May 2005): 1709–35. http://dx.doi.org/10.1142/s0218127405012983.
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Chua's diode is widely used in nonlinear circuit analysis and modeling. In this paper, we propose canonical oscillator models having hysteretic Chua's diodes as their nonlinear elements. Many hysteresis oscillators can be classified into unified groups by using these models. We also present a method for deriving new hysteresis oscillators from known slow–fast (relaxation) oscillators.
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Daniel, E. E., B. L. Bardakjian, J. D. Huizinga, and N. E. Diamant. "Relaxation oscillator and core conductor models are needed for understanding of GI electrical activities." American Journal of Physiology-Gastrointestinal and Liver Physiology 266, no. 3 (March 1, 1994): G339—G349. http://dx.doi.org/10.1152/ajpgi.1994.266.3.g339.
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This review examines the applicability of modeling of intestinal electrical activities (slow waves or pacesetter potentials) by coupled relaxation oscillator models, in comparison to a “multidimensional model” based on core conductor theory. We briefly review the relaxation oscillator model and correct some misunderstandings. We point out that new insights about the role of networks of interstitial cells of Cajal in intestinal pacemaking require reconsideration of the mechanisms producing oscillations, the coupling between oscillators, and how the oscillator network is coupled to the driven cells. Recent advances in relaxation oscillator models allow the production of pacemaking pacemaking activity, which can be selectively varied as to waveform, frequency, and occurrence of silent periods. Core conductor models do not produce pacemaking activity or permit this flexibility. We point out that many of the criticisms leveled against relaxation oscillator models relate to studies made in simplified in vitro systems constrained by extensive dissection. Such systems do not adequately reflect the in vivo systems. We conclude that a full understanding of control of electrical (and mechanical) events in the gastrointestinal tract requires that better understanding of relaxation oscillator models growing out of recent research be combined with improved applications of core conductor theory to multidimensional models.
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Shcherbak, Volodymyr, and Iryna Dmytryshyn. "Tracking the state of pacemakers modeled by the van der Pol equation." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 35 (January 28, 2022): 179–88. http://dx.doi.org/10.37069/1683-4720-2021-35-14.
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It is known that in many applications of physics, biology and other sciences as an approximate dynamic model of complex nonlinear oscillatory processes a model of one or more interconnected van der Pol oscillators or some of its modifications is used \cite{ShD01}. For this reason, nonlinear oscillators are studied as a method of modeling, analysis or even control in various fields, such as electronics \cite{ShD02}, control, robotics \cite{ShD03, ShD04}, biomedical research \cite{ShD05}, geology \cite{ShD06} and others. Naturally, in such modeling there are problems in determining the state and parameters of the models based on the results of measuring the output signals in real time. One of these problems, namely: the problem of determining the state of pacemaker models, which are obtained as certain modifications of the van der Pol oscillator equation, is considered in this paper. In the scientific literature, publications on the modeling of cardiovascular activity using oscillatory systems are widely represented. In recent years, among them there are works that are related to the solution of inverse problems for such models. In particular, in \cite{ShD07} using differential-geometric methods of control theory, a general scheme for constructing asymptotically accurate estimates of the state of a two-dimensional dynamical system is proposed. The obtained results are used to effectively solve the problem of observing two models of pacemakers. In our case in this observation problem we used the method of invariant relations \cite{ShD08}, which was developed in analytical mechanics to find partial solutions (dependencies between variables) in the problems of dynamics of a rigid body with a fixed point. Modification of this method to the problems of control theory, observation, identification allowed to synthesize between known and unknown values of the original system additional connections that arise during the motion of its extended model \cite{ShD09, ShD10, ShD11}. The corresponding technique is to expand the original system by introducing additional controlled differential equations and immersing the original system in a system of greater dimension, which due to its sufficiently free structure is more suitable for constructing an observer or identifier. Controls in an extended system are used to synthesize on its trajectories pre-proposed relations that define the unknown components of the mathematical model (phase vector, parameters) as functions of known quantities. The obtained theoretical results are illustrated by numerical simulations of the corresponding nonlinear observers in Section 5.
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Nosal, W. H., D. W. Thompson, S. Sarkar, A. Subramanian, and J. A. Woollam. "Quantitative oscillator analysis of IR-optical spectra on spin-cast chitosan films." Spectroscopy 19, no. 5,6 (2005): 267–74. http://dx.doi.org/10.1155/2005/498649.
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Infrared optical properties of spin-cast chitosan films have been determined using spectroscopic ellipsometry. Infrared index of refraction and extinction coefficients from 750 cm–1to 4000 cm–1were determined using ellipsometric data fits to dispersion models based on Gaussian shaped oscillators. The free electron contribution was analyzed using a Drude model. This modeling determined that optical anisotropy was present over the entire infrared region. Line shape and oscillator strength analysis was performed to determine oscillator strengths, abundance, and relative bond strength.
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Kim, Valentine, and Roman Parovik. "Mathematical Model of Fractional Duffing Oscillator with Variable Memory." Mathematics 8, no. 11 (November 19, 2020): 2063. http://dx.doi.org/10.3390/math8112063.
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The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann–Liouville type by a discrete analog—the fractional derivative of Grunwald–Letnikov. The adequacy of the numerical scheme is verified using specific examples. Using a numerical algorithm, oscillograms and phase trajectories are constructed depending on the values of the model parameters. Chaotic regimes of the Duffing fractional oscillator are investigated using the Wolf–Bennetin algorithm. The forced oscillations of the Duffing fractional oscillator are investigated using the harmonic balance method. Analytical formulas for the amplitude-frequency, phase-frequency characteristics, and also the quality factor are obtained. It is shown that the fractional Duffing oscillator possesses different modes: regular, chaotic, multi-periodic. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.
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Tass, Peter A. "Estimation of the transmission time of stimulus-locked responses: modelling and stochastic phase resetting analysis." Philosophical Transactions of the Royal Society B: Biological Sciences 360, no. 1457 (May 29, 2005): 995–99. http://dx.doi.org/10.1098/rstb.2005.1635.
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A model of two coupled phase oscillators is studied, where both oscillators are subject to random forces but only one oscillator is repetitively stimulated with a pulsatile stimulus. A pulse causes a reset, which is transmitted to the other oscillator via the coupling. The transmission time of the cross-trial (CT) averaged responses, i.e. the difference in time between the maxima of the CT averaged responses of both oscillators differs from the time difference between the maxima of the oscillators' resets. In fact, the transmission time of the CT averaged responses directly corresponds to the phase difference in the stable synchronized state with integer multiples of the oscillators' mean period added to it. With CT averaged responses it is impossible to reliably estimate the time elapsing, owing to the stimulus' action being transmitted between the two oscillators.
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Narahara, Koichi. "Interaction of Self-Sustained Pulses in Tunnel-Diode Oscillator Lattices." Mathematical Problems in Engineering 2021 (December 15, 2021): 1–14. http://dx.doi.org/10.1155/2021/5027127.
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A one-dimensional lattice in tunnel-diode (TD) oscillators supports self-sustained solitary pulses resulting from the balance between gain and attenuation. By applying the reduction theory to the device’s model equation, it is found that two relatively distant pulses moving in the lattice are mutually affected by a repulsive interaction. This property can be efficiently utilized in equalizing pulse positions to achieve jitter elimination. In particular, when two pulses rotate in a small, closed lattice, they separate evenly at the asymptotic limit. As a result, the lattice loop can provide an efficient platform to obtain low-phase-noise multiphase oscillatory signals. In this work, the interaction between two self-sustained pulses in a TD-oscillator lattice is examined, and the properties of interpulse interaction are validated by conducting several measurements using a test breadboarded lattice.