Phase dynamics of two coupled oscillators under external periodic force

Анищенко, В. С.; Astakhov, Sergey V.; Вадивасова, Т. Е.

doi:10.1209/0295-5075/86/30003

Cited by 62 publications

(56 citation statements)

References 20 publications

(34 reference statements)

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“…The problem of analyzing the driving of two coupled oscillators was recently reconsidered by Anishenko et al [15] who looks for the effects on phase synchronization of two coupled Van der Pol oscillators when they are forced by an external harmonic signal.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of two coupled chaotic systems driven by external signals

Mancini

Vidal

2010

Eur. Phys. J. D

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Abstract. Setting-up a controlled or synchronized state in a space-time chaotic structure targeting an unstable periodic orbit is a key feature of many problems in high dimensional physical, electronics, biological and ecological systems (among others (2000)]. In that case the flow was generated in a small container with inhomogeneous heating in order to have a single roll structure produced by a Bénard-Marangoni instability [E.L. Koshmieder, Bénard Cells and Taylor Vortices (Cambridge University Press, 1993)]. Phase synchronization was achieved by a small amplitude signal injected at a subharmonic frequency obtained from the measured Fourier temperature spectrum. In this work, we analyze numerically the effects of driving two previously synchronized chaotic oscillators by an external signal. The numerical system represents a convective experiment in a small container with square symmetry, where boundary layer instabilities are coupled by a common flow. This work is an attempt to control this situation and overcome some difficulties to select useful frequency values for the driving force, analyzing the influence of different harmonic injection signals on the synchronization in a system composed by two identical chaotic Takens-Bogdanov equations (TBA and TBB) bidirectionally coupled.

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Section: Introductionmentioning

confidence: 99%

Dynamics of two coupled chaotic systems driven by external signals

Mancini

Vidal

2010

Eur. Phys. J. D

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“…The dynamics of a single free-running GO can be studied using the system Equation (4). Now in the system of BCGO, a fraction of the output of a GO is injected into the other GO.…”

Section: Derivation Of System Equationsmentioning

confidence: 99%

“…But at the same time a complete understanding of the dynamics of such systems is a formidable problem from analytical point of view. In electronic engineering in general and communication technology in particular, the importance of coupled oscillators has been underscored by several researchers [4][5][6][7], as they are useful in the problems related to stable signal generation and synchronous amplification in RF and Microwave (MW) communication systems.…”

Section: Introductionmentioning

confidence: 99%

Studies on the Dynamics of Bilaterally Coupled X-Band Gunn Oscillators

Sarkar¹,

Sarkar²,

Sarkar³

et al. 2011

PIER B

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Abstract-The dynamics of a system comprising of two bilaterally coupled Gunn oscillators (BCGOs) has been examined using a circuit theoretic model of the Gunn oscillator (GO). The effects of coupling factors (k ij ) between i-th and j-th oscillators on the frequency-range of synchronized operation and the magnitude of common frequency of oscillation have been examined semi-analytically and by numerical solution of the system equations. The occurrence of chaotic oscillations at the verge of synchronization bands is observed in numerical simulation. The experimental response of the BCGO operating in the X-band is obtained and the results are found to be qualitatively similar to the analytical and numerical predictions.

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“…The first one is a global coupling, where all-to-all coupling is present, hence the oscillators are connected with each other by direct links or by the mean field [1][2][3][4]. The second type is a local coupling, where the single oscillator is connected to nodes in its nearest neighborhood [5][6][7][8][9][10]. In this work we consider the local coupling.…”

Section: Introductionmentioning

confidence: 99%

Multistability in nonlinearly coupled ring of Duffing systems

Jaros

Kapitaniak

Perlikowski

2016

Eur. Phys. J. Spec. Top.

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Abstract. In this paper we consider dynamics of three unidirectionally coupled Duffing oscillators with nonlinear coupling function in the form of third degree polynomial. We focus on the influence of the coupling on the occurrence of different bifurcation's scenarios. The stability of equilibria, using Routh-Hurwitz criterion, is investigated. Moreover, we check how coefficients of the nonlinear coupling influence an appearance of different types of periodic solutions. The stable periodic solutions are computed using path-following. Finally, we show the two parameters' bifurcation diagrams with marked areas where one can observe the coexistence of solutions.

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Phase dynamics of two coupled oscillators under external periodic force

Cited by 62 publications

References 20 publications

Dynamics of two coupled chaotic systems driven by external signals

Dynamics of two coupled chaotic systems driven by external signals

Studies on the Dynamics of Bilaterally Coupled X-Band Gunn Oscillators

Multistability in nonlinearly coupled ring of Duffing systems

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