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Journal articles on the topic 'Driven chaotic oscillators'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

GAO, JIAN, and ZHIGANG ZHENG. "PHASE SYNCHRONIZATION IN DOUBLY DRIVEN CHAOTIC OSCILLATORS." International Journal of Modern Physics B 18, no. 20n21 (2004): 2945–52. http://dx.doi.org/10.1142/s021797920402535x.

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Phase synchronization of a chaotic oscillator that is driven by two chaotic signals is investigated. The anti-biased PS in the presence of biased coupling is found, i.e., the response oscillator can be phase synchronized by the drive with a weaker coupling rather than the stronger driver. The mechanism for this behavior is explored. In the non-PS region, alternating phase-locking is observed.

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2

KYPRIANIDIS, I. M., CH VOLOS, I. N. STOUBOULOS, and J. HADJIDEMETRIOU. "DYNAMICS OF TWO RESISTIVELY COUPLED DUFFING-TYPE ELECTRICAL OSCILLATORS." International Journal of Bifurcation and Chaos 16, no. 06 (2006): 1765–75. http://dx.doi.org/10.1142/s0218127406015660.

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Duffing-type electrical oscillator is a second-order nonlinear electric circuit driven by a sinusoidal voltage source. The nonlinear element is a nonlinear inductor. We have studied the dynamics of two resistively coupled oscillators of this type in two cases. The first, when the oscillators are identical having chaotic dynamics, and the second, when the oscillators are in different dynamic states (periodic and chaotic, respectively). In the first case, chaotic synchronization is observed, while in the second case control of the chaotic behavior is achieved.

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3

HUANG, XIA, JIAN GAO, DAIHAI HE, and ZHIGANG ZHENG. "GENERALIZED SYNCHRONIZATION IN DOUBLY DRIVEN CHAOTIC SYSTEM." International Journal of Modern Physics B 20, no. 24 (2006): 3477–85. http://dx.doi.org/10.1142/s0217979206035540.

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Generalized synchronization (GS) of a chaotic oscillator driven by two chaotic signals is investigated in this paper. Both receiver and drivers are the same kind of oscillators with mismatched parameter values. Partial and global GS may appear depending on coupling strengths. An approach based on the conditional entropy analysis is presented to test the partial GS, which is difficult to determine with conventional methods. A trough in conditional entropy spectrum indicates partial GS between the receiver and one of the drivers.

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4

Ritala, R. K. "Chaotic Dynamics of Nonideally Driven Simple Oscillators." Physica Scripta T9 (January 1, 1985): 70–75. http://dx.doi.org/10.1088/0031-8949/1985/t9/010.

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5

Marshall, Delmar, and J. C. Sprott. "Simple driven chaotic oscillators with complex variables." Chaos: An Interdisciplinary Journal of Nonlinear Science 19, no. 1 (2009): 013124. http://dx.doi.org/10.1063/1.3080193.

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6

LEI, YOUMING, and FULI GUAN. "DISORDER INDUCED ORDER IN AN ARRAY OF CHAOTIC DUFFING OSCILLATORS." International Journal of Modern Physics C 23, no. 10 (2012): 1250071. http://dx.doi.org/10.1142/s0129183112500714.

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This paper addresses the issue of disorder induced order in an array of coupled chaotic Duffing oscillators which are excited by harmonic parametric excitations. In order to investigate the effect of phase disorder on dynamics of the array, we take into account that individual uncoupled Duffing oscillator with a parametric excitation is chaotic no matter what the initial phase of the excitation is. It is shown that phase disorder by randomly choosing the initial phases of excitations can suppress spatio-temporal chaos in the system coupled by chaotic Duffing oscillators. When all the phases ar

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7

TYRKIEL, ELŻBIETA. "ON THE ROLE OF CHAOTIC SADDLES IN GENERATING CHAOTIC DYNAMICS IN NONLINEAR DRIVEN OSCILLATORS." International Journal of Bifurcation and Chaos 15, no. 04 (2005): 1215–38. http://dx.doi.org/10.1142/s0218127405012727.

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In the paper, the most important common dynamical element underlying the build-up of chaotic responses in nonlinear vibrating systems, i.e. the formation and expansion of invariant non-attracting chaotic sets, so-called chaotic saddles, as a result of transverse intersections of stable and unstable invariant manifolds of particular unstable orbits, is highlighted. Characteristic examples of the resulting multiple aspects of chaotic system behaviors, such as chaotic transient motions, fractal basin boundaries and unpredictability of the final state, are shown and discussed with the use of geome

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8

Rosenblum, M. G., A. S. Pikovsky, and J. Kurths. "Phase synchronization in driven and coupled chaotic oscillators." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44, no. 10 (1997): 874–81. http://dx.doi.org/10.1109/81.633876.

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9

ITOH, MAKOTO, HIROYUKI MURAKAMI, and LEON O. CHUA. "EXPERIMENTAL STUDY OF FORCED CHUA’S OSCILLATOR." International Journal of Bifurcation and Chaos 04, no. 06 (1994): 1721–42. http://dx.doi.org/10.1142/s0218127494001349.

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Chua’s oscillator driven by an external current source is studied. Our experimental study reveals the following rich variety of interesting bifurcation phenomena: (a) period adding; (b) frequency entrainment of chaos; (c) torus breakdown to chaos; (d) chaotic attractors with strange geometrical patterns; (e) regularity of periodic windows; (f) coexistence of multiple attractors; (g) period-preserving bifurcations; (h) large-sized chaotic attractors; (i) intermittent behavior. Furthermore, some interesting applications of the forced Chua’s oscillators are suggested.

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10

DANA, SYAMAL KUMAR, BRAJENDRA K. SINGH, SATYABRATA CHAKRABORTY, et al. "MULTISCROLL IN COUPLED DOUBLE SCROLL TYPE OSCILLATORS." International Journal of Bifurcation and Chaos 18, no. 10 (2008): 2965–80. http://dx.doi.org/10.1142/s0218127408022196.

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A unidirectional coupling scheme is investigated in double scroll type chaotic oscillators that reveal interesting multiscroll dynamics. Instead of using self-oscillatory systems, in this scheme, double scroll chaos from one oscillator is forced into another similar oscillator in a resting state. This coupling scheme is explored in the Chua oscillator, a modified Chua oscillator and the Lorenz oscillator. We have modified the Chua oscillator by simply changing its piecewise linear function slightly, thereby deriving a new 3-scroll attractor. We have observed 4-scroll, 6-scroll attractors in th

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11

Glod, Lukáš, Gabriela Vasziová, Jana Tóthová, and Vladimír Lisý. "Brownian Oscillators Driven by Correlated Noise in a Moving Trap." Journal of Electrical Engineering 63, no. 1 (2012): 53–58. http://dx.doi.org/10.2478/v10187-012-0008-8.

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Brownian Oscillators Driven by Correlated Noise in a Moving TrapBrownian oscillator, ie a micron-sized or smaller particle trapped in a thermally fluctuating environment is studied. The confining harmonic potential can move with a constant velocity. As distinct from the standard Langevin theory, the chaotic force driving the particle is correlated in time. The dynamics of the particle is described by the generalized Langevin equation with the inertial term, a coloured noise force, and a memory integral. We consider two kinds of the memory in the system. The first one corresponds to the exponen

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12

Uhm, Wonsuhk, and Seunghwan Kim. "Phase synchronization and crisis in coupled periodically driven chaotic oscillators." Physics Letters A 327, no. 2-3 (2004): 167–73. http://dx.doi.org/10.1016/j.physleta.2004.05.024.

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13

Wu Yu-Xi, Huang Xia, Gao Jian, and Zheng Zhi-Gang. "Phase synchronization and generalized synchronization in doubly driven chaotic oscillators." Acta Physica Sinica 56, no. 7 (2007): 3803. http://dx.doi.org/10.7498/aps.56.3803.

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14

ITOH, MAKOTO, TAO YANG, and LEON O. CHUA. "EXPERIMENTAL STUDY OF IMPULSIVE SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC CIRCUITS." International Journal of Bifurcation and Chaos 09, no. 07 (1999): 1393–424. http://dx.doi.org/10.1142/s0218127499000961.

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In this paper, experimental results on impulsive synchronization of two kinds of chaotic circuits; namely, Chua's oscillator and a hyperchaotic circuit, are presented. To impulsively synchronize two Chua's oscillators, synchronization impulses sampled from one state variable of the driving circuit are transmitted to the driven circuit. To impulsively synchronize two hyperchaotic circuits, synchronizing impulses sampled from two signals of the driving circuit are sent to the driven circuit. Our experimental results show that the accuracy of impulsive synchronization depends on both the period a

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15

HUGUES-SALAS, O., and S. P. BANKS. "OPTIMAL CONTROL OF CHAOS IN NONLINEAR DRIVEN OSCILLATORS VIA LINEAR TIME-VARYING APPROXIMATIONS." International Journal of Bifurcation and Chaos 18, no. 11 (2008): 3355–74. http://dx.doi.org/10.1142/s0218127408022421.

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An optimal chaos control procedure is proposed. The aim of using this method is to stabilize the chaotic behavior of forced continuous-time nonlinear systems by using an approximation sequence technique and linear optimal control. The idea of the approximation technique is to use a sequence of linear, time-varying equations to approximate the solution of nonlinear systems. In each of these equations, the linear-quadratic optimal tracking control is applied. The purpose is to find a linear time-varying feedback controller which produces an optimized trajectory that converges to a desired signal

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16

dos Santos, Ângela Maria, Sérgio Roberto Lopes, and Ricardo Luiz Viana. "Intermittent Behavior and Synchronization of Two Coupled Noisy Driven Oscillators." Mathematical Problems in Engineering 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/610574.

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The coupled system of two forced Liénard-type oscillators has applications in diode-based electric circuits and phenomenological models for the heartbeat. These systems typically exhibit intermittent transitions between laminar and chaotic states; what affects their performance and, since noise is always present in such systems, dynamical models should include these effects. Accordingly, we investigated numerically the effect of noise in two intermittent phenomena: the intermittent transition to synchronized behavior for identical and unidirectionally coupled oscillators, and the intermittent

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17

TÔRRES, LEONARDO A. B., and LUIS ANTONIO AGUIRRE. "PCCHUA — A LABORATORY SETUP FOR REAL-TIME CONTROL AND SYNCHRONIZATION OF CHAOTIC OSCILLATIONS." International Journal of Bifurcation and Chaos 15, no. 08 (2005): 2349–60. http://dx.doi.org/10.1142/s0218127405013356.

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This paper describes a laboratory setup suitable for implementing low cost real-time solutions in the fields of control, synchronization and information transmission based on chaotic oscillators. The setup has the following features: (a) it is composed of a Chua oscillator furnished with three actuators thus permitting mono- and multi-variable control; (b) the actuators can be driven by the analog outputs of a standard I/O-board; in order to be able to actuate fast enough (c) the I/O-board is driven by a real time program written for Linux and (d) an inductorless implementation of Chua's circu

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18

ALVAREZ-LLAMOZA, O., and M. G. COSENZA. "SYNCHRONIZATION INDUCED BY INTERMITTENT VERSUS PARTIAL DRIVES IN CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 20, no. 02 (2010): 323–30. http://dx.doi.org/10.1142/s0218127410025776.

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We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization behavior of both systems can be inferred by considering the dynamics of a single chaotic map driven with a probability p. The synchronized states for these systems are characterized on their common space of parameters. Our results show that the presence of a common external drive for all times is not essential for reaching synchronization in a system of cha

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19

Butusov, Denis, Timur Karimov, Alexander Voznesenskiy, Dmitry Kaplun, Valery Andreev, and Valerii Ostrovskii. "Filtering Techniques for Chaotic Signal Processing." Electronics 7, no. 12 (2018): 450. http://dx.doi.org/10.3390/electronics7120450.

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The vulnerability of chaotic communication systems to noise in transmission channel is a serious obstacle for practical applications. Traditional signal processing techniques provide only limited possibilities for efficient filtering broadband chaotic signals. In this paper, we provide a comparative study of several denoising and filtering approaches: a recursive IIR filter, a median filter, a wavelet-based denoising method, a method based on empirical modes decomposition, and, finally, propose the new filtering algorithm based on the cascade of driven chaotic oscillators. Experimental results

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20

ERDMANN, UDO, and WERNER EBELING. "ON THE ATTRACTORS OF TWO-DIMENSIONAL RAYLEIGH OSCILLATORS INCLUDING NOISE." International Journal of Bifurcation and Chaos 15, no. 11 (2005): 3623–33. http://dx.doi.org/10.1142/s0218127405014271.

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We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular, we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops severa

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21

Tajik, Fatemeh, Zahra Babamahdi, Mehdi Sedighi, and George Palasantzas. "Nonlinear Actuation of Casimir Oscillators toward Chaos: Comparison of Topological Insulators and Metals." Universe 7, no. 5 (2021): 123. http://dx.doi.org/10.3390/universe7050123.

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In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are currently used in devices. Bifurcation and phase portraits analysis in conservative systems suggest that the strong difference between the conduction states of Bi2Se3 and Au yields sufficiently weaker Casimir force to enhance stable operation. Furthermore, for nonconservative driven systems, the Melnikov function and Poincare portrait an

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22

TSANG, KWOK YEUNG, and IRA B. SCHWARTZ. "RECURRING ANTI-PHASE SIGNALS IN COUPLED NONLINEAR OSCILLATORS: CHAOTIC OR RANDOM TIME SERIES?" International Journal of Bifurcation and Chaos 03, no. 03 (1993): 773–78. http://dx.doi.org/10.1142/s0218127493000684.

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We discovered the existence of a new type of high-dimensional attractor in coupled nonlinear oscillator systems. Due to the presence of neutrally stable directions on the attractor, there can be noise-driven phase space diffusion. Recurring anti-phase states are observed as coherent portions of the time series. The observed time series looks coherent for a while, then incoherent, and then coherent again. Although the time series “looks” chaotic, the Lyapunov exponents are not positive.

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23

Warminski, Jerzy. "Regular and Chaotic Vibrations of Van Der Pol and Rayleigh Oscillators Driven by Parametric Excitation." Procedia IUTAM 5 (2012): 78–87. http://dx.doi.org/10.1016/j.piutam.2012.06.011.

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24

Takougang Kingni, Sifeu, Jimmi Hervé Talla Mbé, and Paul Woafo. "Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography." Chaos: An Interdisciplinary Journal of Nonlinear Science 22, no. 3 (2012): 033108. http://dx.doi.org/10.1063/1.4733702.

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25

Kenmogne, Fabien, Samuel Noubissie, Guy Bertrand Ndombou, Eric Tala Tebue, Armel Viquit Sonna, and David Yemélé. "Dynamics of two models of driven extended jerk oscillators: Chaotic pulse generations and application in engineering." Chaos, Solitons & Fractals 152 (November 2021): 111291. http://dx.doi.org/10.1016/j.chaos.2021.111291.

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26

Sedighi, M., F. Tajik, S. M. Mahmoudi, M. H. Nazarpak, G. R. R. Lamouki, and G. Palasantzas. "Sensitivity of Casimir oscillators on geometry and optical properties." Modern Physics Letters A 35, no. 03 (2020): 2040003. http://dx.doi.org/10.1142/s0217732320400039.

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The dependence of the Casimir force on the optical properties and geometry of interacting materials makes possible to tailor the actuation dynamics of micro/nano actuators. In this research, we study the dynamical sensitivity of micro- and nanoelectromechanical systems on geometry by comparing the plate-plate and sphere-plate configurations, and taking into account the optical properties of the interacting materials. In fact, for conservative systems bifurcation analysis and phase portraits show that the geometry and the optical properties strongly influence the stability of an actuating devic

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27

Simiu, E. "Melnikov Process for Stochastically Perturbed, Slowly Varying Oscillators: Application to a Model of Wind-Driven Coastal Currents." Journal of Applied Mechanics 63, no. 2 (1996): 429–35. http://dx.doi.org/10.1115/1.2788884.

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The stochastic Melnikov approach is extended to a class of slowly varying dynamical systems. It is found that (1) necessary conditions for chaos induced by stochastic perturbations depend on the excitation spectrum and the transfer function in the expression for the Melnikov transform; (2) the Melnikov approach allows the estimation of lower bounds for (a) the mean time of exit from preferred regions of phase space, and (b) the probability that exits from those regions cannot occur during a specified time interval. For a system modeling wind-induced currents, the deterministic Melnikov approac

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28

Danao Adile Adoum, Ali Ramadan, Samuel Noubissié, et al. "Dynamics of a discontinuous coupled electro-mechanical system oscillator with strong irrational nonlinearities and with two outputs." Global Journal of Engineering and Technology Advances 6, no. 1 (2021): 116–35. http://dx.doi.org/10.30574/gjeta.2021.6.1.0301.

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The dynamics of the nonlinear electromechanical device, consisting of a mechanical part with two outputs and an electrical part which acts as the server is strongly investigated in the present work. The mechanical part consists of two nonlinear oscillators with strong irrational nonlinearities having smooth or discontinuous characteristics, where nonlinearity is just due to the inclination of springs, the geometric configuration, which are both elastically coupled. While the electrical part is the Rayleigh equation. By using the Lagrangian formulation, the model equations are established and u

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29

Talla, F. Calvin, Robert Tchitnga, P. H. Louodop Fotso, Romanic Kengne, Bonaventure Nana, and Anaclet Fomethe. "Unexpected Behaviors in a Single Mesh Josephson Junction Based Self-Reproducing Autonomous System." International Journal of Bifurcation and Chaos 30, no. 07 (2020): 2050097. http://dx.doi.org/10.1142/s0218127420500972.

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In the literature, existing Josephson junction based oscillators are mostly driven by external sources. Knowing the different limits of the external driven systems, we propose in this work a new autonomous one that exhibits the unusual and striking multiple phenomena among which coexist the multiple hidden attractors in self-reproducing process under the effect of initial conditions. The eight-term autonomous chaotic system has a single nonlinearity of sinusoidal type acting on only one of the state variables. A priori, the simplicity of the system does not predict the richness of its dynamics

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30

Селезнев, Е. П., та Н. В. Станкевич. "Сложная динамика неавтономного осциллятора с управляемой фазой внешнего воздействия". Письма в журнал технической физики 45, № 2 (2019): 59. http://dx.doi.org/10.21883/pjtf.2019.02.47227.17473.

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AbstractThe dynamics of a non-autonomous oscillator in which the phase of external force linearly depends on a dynamic variable has been investigated. This control of the external-drive phase leads to the formation of a hierarchy of various periodic and chaotic oscillations. The structure of the space of control parameters has been studied. It is established that dynamics of the system exhibits oscillatory regimes analogous to those of a non-autonomous oscillator with potential in the form of a periodic function.

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31

Liu, Ruonan, Yanmei Kang, Yuxuan Fu, and Guanrong Chen. "Stochastic Resonance and Bifurcation of Order Parameter in a Coupled System of Underdamped Duffing Oscillators." International Journal of Bifurcation and Chaos 29, no. 08 (2019): 1950108. http://dx.doi.org/10.1142/s0218127419501086.

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The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type [Formula: see text]-theorem is proved for the associated nonlinear Fokker–Planck equation to ensure that the system can always be relaxed to one of the stationary states as time is long enough. Based on a general framework of the linear response theory, the linear dynamical susceptibility of the system order parameter is explicitly deduced. With the spectral amplification factor as a quantifying index, calculation by the method

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32

Schumacher, Johannes, Thomas Wunderle, Pascal Fries, Frank Jäkel, and Gordon Pipa. "A Statistical Framework to Infer Delay and Direction of Information Flow from Measurements of Complex Systems." Neural Computation 27, no. 8 (2015): 1555–608. http://dx.doi.org/10.1162/neco_a_00756.

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In neuroscience, data are typically generated from neural network activity. The resulting time series represent measurements from spatially distributed subsystems with complex interactions, weakly coupled to a high-dimensional global system. We present a statistical framework to estimate the direction of information flow and its delay in measurements from systems of this type. Informed by differential topology, gaussian process regression is employed to reconstruct measurements of putative driving systems from measurements of the driven systems. These reconstructions serve to estimate the dela

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33

Cusumano, J. P., and D. C. Lin. "Bifurcation and Modal Interaction in a Simplified Model of Bending-Torsion Vibrations of the Thin Elastica." Journal of Vibration and Acoustics 117, no. 1 (1995): 30–42. http://dx.doi.org/10.1115/1.2873864.

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This paper presents a numerical study of bifurcation and modal interaction in a system of partial differential equations first proposed as a simplified model for bending-torsion vibrations of a thin elastic beam. A system of seven ordinary differential equations obtained using the first six bending and first torsional normal modes is studied, and Floquet theory is used to locate regions in the forcing frequency, forcing amplitude parameter plane where “planar” (i.e., zero torsion) motions are unstable. Numerical branch following and symmetry considerations show that the initial instability ari

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34

Karthikeyan, Anitha, Karthikeyan Rajagopal, Victor Kamdoum Tamba, Girma Adam, and Ashokkumar Srinivasan. "A Simple Chaotic Wien Bridge Oscillator with a Fractional-Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability." Complexity 2021 (March 1, 2021): 1–13. http://dx.doi.org/10.1155/2021/8857075.

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Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which us

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35

Husbands, Phil, Yoonsik Shim, Michael Garvie, et al. "Recent advances in evolutionary and bio-inspired adaptive robotics: Exploiting embodied dynamics." Applied Intelligence 51, no. 9 (2021): 6467–96. http://dx.doi.org/10.1007/s10489-021-02275-9.

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AbstractThis paper explores current developments in evolutionary and bio-inspired approaches to autonomous robotics, concentrating on research from our group at the University of Sussex. These developments are discussed in the context of advances in the wider fields of adaptive and evolutionary approaches to AI and robotics, focusing on the exploitation of embodied dynamics to create behaviour. Four case studies highlight various aspects of such exploitation. The first exploits the dynamical properties of a physical electronic substrate, demonstrating for the first time how component-level ana

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36

TÖBBENS, ALEXANDER, ROBERT METTIN, and ULRICH PARLITZ. "DYNAMICS OF A DRIVEN OSCILLATOR CARRYING A FREELY SLIDING MASS." International Journal of Bifurcation and Chaos 22, no. 06 (2012): 1250132. http://dx.doi.org/10.1142/s0218127412501325.

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A mathematical model for a nonlinear oscillator, which is composed of an oscillating mass interacting with a freely sliding friction damper, is introduced and investigated. This oscillator is a strongly simplified model for a damping principle applied to turbine blades to suppress oscillations induced by inhomogeneous flow fields. It exhibits periodic, quasi-periodic, as well as chaotic dynamics occuring suddenly due to adding sliding bifurcations. Mathematically, the oscillator is given as a piecewise smooth (Filippov) system with a switching manifold corresponding to the sticking phase of th

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37

Anastasio, D., A. Fasana, L. Garibaldi, and S. Marchesiello. "Nonlinear Dynamics of a Duffing-Like Negative Stiffness Oscillator: Modeling and Experimental Characterization." Shock and Vibration 2020 (May 15, 2020): 1–13. http://dx.doi.org/10.1155/2020/3593018.

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In this paper, a negative stiffness oscillator is modelled and tested to exploit its nonlinear dynamical characteristics. The oscillator is part of a device designed to improve the current collection quality in railway overhead contact lines, and it acts like an asymmetric double-well Duffing system. Thus, it exhibits two stable equilibrium positions plus an unstable one, and the oscillations can either be bounded around one stable point (small oscillations) or include all the three positions (large oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinea

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38

Gottlieb, H. P. W., and J. C. Sprott. "Simplest driven conservative chaotic oscillator." Physics Letters A 291, no. 6 (2001): 385–88. http://dx.doi.org/10.1016/s0375-9601(01)00765-4.

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KAISER, F., and C. EICHWALD. "BIFURCATION STRUCTURE OF A DRIVEN, MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR (I): THE SUPERHARMONIC RESONANCE STRUCTURE." International Journal of Bifurcation and Chaos 01, no. 02 (1991): 485–91. http://dx.doi.org/10.1142/s0218127491000385.

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Bifurcations in the superharmonic region of a generalized version of the van der Pol oscillator which exhibits three limit cycles are investigated. An external force causes the subsequent breakdown of the self-sustained oscillations. Beyond these series of bifurcations chaotic solutions also exist. In this first part we concentrate on a discussion of the bifurcation structure of the system.

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Cooper, D. P., and E. Schöll. "Tunable Real Space Transfer Oscillator by Delayed Feedback Control of Chaos." Zeitschrift für Naturforschung A 50, no. 2-3 (1995): 117–24. http://dx.doi.org/10.1515/zna-1995-2-301.

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Abstract It is demonstrated numerically that by using Pyragas' method of chaos self-control a stable semiconductor oscillator can be designed based on driven real-space transfer oscillations in a modulation-doped heterostructure. By application of a small time-continuous delayed feedback voltage control signal, different unstable periodic orbits embedded in the chaotic attractor can be stabilized. Thus different modes of self-generated periodic voltage oscillations can be selected by choosing an appropriate delay time. This provides tunability to different discrete frequencies.

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EICHWALD, C., and F. KAISER. "BIFURCATION STRUCTURE OF A DRIVEN MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR (II): SYMMETRY-BREAKING CRISIS AND INTERMITTENCY." International Journal of Bifurcation and Chaos 01, no. 03 (1991): 711–15. http://dx.doi.org/10.1142/s021812749100052x.

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Bifurcations in the superharmonic region of a generalized version of the van der Pol oscillator which exhibits three limit cycles are investigated. An external force causes the subsequent breakdown of the self-sustained oscillations. Beyond these series of bifurcations chaotic solutions also exist. They display a symmetry-breaking crisis followed by a type III intermittency transition. The bifurcations are discussed with respect to the symmetry properties of chaotic attractors. The critical exponents connected with the bifurcations offer a scaling which partially contradicts that known from li

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LICHTENBERG, A. J., and A. M. MARAKHTANOV. "BIFURCATION AND CHAOTIC TRANSITION TO RELAXATION OSCILLATIONS IN AN INDUCTIVELY DRIVEN ELECTRONEGATIVE PLASMA." International Journal of Bifurcation and Chaos 15, no. 08 (2005): 2623–31. http://dx.doi.org/10.1142/s0218127405013563.

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Regular and chaotic relaxation oscillations in charged particle densities, light and floating potential are seen in low-pressure inductive discharges, in the transition between lower power capacitive operation and higher power inductive operation, if the plasma is electronegative, i.e. contains negative ions. As pressure or power is varied to cross a threshold, either from stable capacitive or stable inductive operation, the instability goes through a series of oscillatory, sometimes chaotic, states to large scale relaxation oscillations between higher and lower densities. A volume-averaged mo

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YAMAPI, R., B. R. NANA NBENDJO, and H. G. ENJIEU KADJI. "DYNAMICS AND ACTIVE CONTROL OF MOTION OF A DRIVEN MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR." International Journal of Bifurcation and Chaos 17, no. 04 (2007): 1343–54. http://dx.doi.org/10.1142/s0218127407017847.

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This paper deals with the dynamics and active control of a driven multi-limit-cycle Van der Pol oscillator. The amplitude of the oscillatory states both in the autonomous and nonautonomous case are derived. The interaction between the amplitudes of the external excitation and the limit-cycles are also analyzed. The domain of the admissible values on the amplitude for the external excitation is found. The effects of the control parameter on the behavior of a driven multi-limit-cycle Van der Pol model are analyzed and it appears that with the appropriate selection of the coupling parameter, the

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Zhou, Liang Qiang, and Fang Qi Chen. "Chaotic Motions of a Damped and Driven Morse Oscillator." Applied Mechanics and Materials 459 (October 2013): 505–10. http://dx.doi.org/10.4028/www.scientific.net/amm.459.505.

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With the Melnikov method and numerical methods, this paper investigate the chaotic motions of a damped and driven morse oscillator. The critical curves separating the chaotic and non-chaotic regions are obtained, which demonstrate that when the Morse spectroscopic term is fixed, for the case of large values of the period of the excitation, the critical value for chaotic motions decreases as the dissociation energy increases; while for the case of small values of the period of the excitation, the critical value for chaotic motions increases as the dissociation energy increases. It is also shown

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PANDE, M. B., RANJIT SINGH, and S. DUTTA GUPTA. "CHAOS IN A PIECEWISE LINEAR SYSTEM UNDER FREQUENCY SWITCHING." International Journal of Bifurcation and Chaos 04, no. 03 (1994): 701–7. http://dx.doi.org/10.1142/s0218127494000496.

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We investigate the dynamics of an oscillator with gain with switching between two cosinusoidal drives. The drive is assumed to be dependent on the state of the system and its prehistory. We show that frequency switching alone can lead to a chaotic response. Moreover, we demonstrate that resonance phenomena inhibit chaos and lead to unbounded motion. We also point out the crucial role played by the initial phases of the drives.

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Wang, Ke, Xiaopeng Yan, Zhiqiang Zhu, Xinhong Hao, Ping Li, and Qian Yang. "Blind Estimation Methods for BPSK Signal Based on Duffing Oscillator." Sensors 20, no. 22 (2020): 6412. http://dx.doi.org/10.3390/s20226412.

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To realize the blind estimation of binary phase shift keying (BPSK) signal, this paper describe a new relational expression among the state of Duffing oscillator excited by BPSK signal, the pseudo-random code of BPSK signal, and the difference frequency between the to-be-detect signal and internal drive force signal of Duffing oscillator. Two output characteristics of Duffing oscillators excited by BPSK signals named implied periodicity and pilot frequency array synchronization are presented according to the different chaotic states of Duffing oscillator. Then two blind estimation methods for

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Balibrea, Francisco, Ricardo Chacón, and Miguel Angel López. "Inhibition of Chaotic Escape by an Additional Driven Term." International Journal of Bifurcation and Chaos 08, no. 08 (1998): 1719–23. http://dx.doi.org/10.1142/s0218127498001406.

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In this paper, we are devoted to the problem of escaping from a potential well which is present in a great number of physical situations. We use the Helmholtz oscillator as a model for those situations and consider the behavior of the oscillator under an additional driven perturbation. The Melnikov analysis reveals it as an adequate method. Some comparisons are made with the perturbations of the oscillator on the linear and quadratic terms.

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Sun, Junwei, Chun Huang, and Guangzhao Cui. "Hybrid Dislocated Control and General Hybrid Projective Dislocated Synchronization for Memristor Chaotic Oscillator System." Advances in Mathematical Physics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/563172.

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Some important dynamical properties of the memristor chaotic oscillator system have been studied in the paper. A novel hybrid dislocated control method and a general hybrid projective dislocated synchronization scheme have been realized for memristor chaotic oscillator system. The paper firstly presents hybrid dislocated control method for stabilizing chaos to the unstable equilibrium point. Based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization has been studied for the drive memristor chaotic oscillator system and the same response memristor chaotic osci

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Kingston, S. Leo, and K. Thamilmaran. "Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System." International Journal of Bifurcation and Chaos 27, no. 07 (2017): 1730025. http://dx.doi.org/10.1142/s0218127417300257.

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We report the existence of bursting oscillations and mixed-mode oscillations in a Liénard system when it is driven externally by a sinusoidal force. The bursting oscillations transit from a periodic phase to spiking trains through chaotic windows, as the control parameter is varied. The mixed-mode oscillations appear via an alternate sequence of periodic and chaotic states, as well as Farey sequences. The primary and their associated secondary mixed-mode oscillations are detected for the suitable choices of system parameters. Additionally, the system is also found to possess multistability nat

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Bryant, Peter J., and John W. Miles. "On a periodically forced, weakly damped pendulum. Part 2: Horizontal forcing." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32, no. 1 (1990): 23–41. http://dx.doi.org/10.1017/s0334270000008195.

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AbstractWe consider the phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum driven by horizontal, periodic forcing of the pivot with maximum acceleration εg and dimensionless frequency ω. Analytical solutions for symmetric oscillations at smaller values of ε are continued into numerical solutions at larger values of ε. A wide range of stable oscillatory solutions is described, including motion that is symmetric or asymmetric, downward or inverted, and at periods equal to the forcing period T ≡ 2π/ω or integral multiples thereof. Stable runnin

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