Chaos crisis in coupled Duffing's systems with initial phase difference

Bi, Qinsheng

doi:10.1016/j.physleta.2007.02.101

Cited by 7 publications

(2 citation statements)

References 17 publications

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“…Coupled oscillators have been intensively studied in various disciplines because they have a variety of applications, including pattern recognition, biological information processing, and control. [1][2][3][4][5][6][7] Very recently, the dynamics of special networks of coupled oscillators has received particular attention in the literature. [8][9][10][11] In Ref.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Jiang

Zhang

2015

Chinese Phys. B

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Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.

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Section: Introductionmentioning

confidence: 99%

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Jiang

Zhang

2015

Chinese Phys. B

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“…On the other hand, coupled oscillators can exhibit many complex dynamical behaviors, so the dynamics of coupled oscillators have received particular attention in the literature [2][3][4]. Synchronization is a kind of typical collective behavior and basic motion in nature.…”

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confidence: 99%

Contraction theory based synchronization analysis of impulsively coupled oscillators

Jiang

2011

Nonlinear Dyn

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Impulsively coupled oscillators which are assumed to interact with each other only at discrete times have many applications in practice. In this paper, we introduce the concept of partial contraction theory of impulsive systems, which is used to investigate the synchronization problem of impulsively coupled oscillators. Contraction analysis of two impulsively coupled oscillators and networked impulsively coupled oscillators is provided, respectively. Very simple but very general results for synchronization of impulsively coupled oscillators are derived. Numerical simulations show the effectiveness of our theoretical results.

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Realizing hybrid synchronization of time-delay hyperchaotic 4D systems via partial variables

Wang

Shi

et al. 2014

Applied Mathematics and Computation

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Chaos crisis in coupled Duffing's systems with initial phase difference

Cited by 7 publications

References 17 publications

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Contraction theory based synchronization analysis of impulsively coupled oscillators

Realizing hybrid synchronization of time-delay hyperchaotic 4D systems via partial variables

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