STABILITY, SYMMETRY-BREAKING BIFURCATIONS AND CHAOS IN DISCRETE DELAYED MODELS

Author:

PENG MINGSHU1,YUAN YUAN2

Affiliation:

1. Department of Mathematics, Beijing Jiao Tong University, Beijing 100 044, P. R. China

2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

Abstract

In this paper, we use the standard bifurcation theory to study rich dynamics of time-delayed coupling discrete oscillators. Equivariant bifurcations including equivariant Neimark–Sacker bifurcation, equivariant pitchfork bifurcation and equivariant periodic doubling bifurcation are analyzed in detail. In the application, we consider a ring of identical discrete delayed Ikeda oscillators. Multiple oscillation patterns, such as multiple stable equilibria, stable limit cycles, stable invariant tori and multiple chaotic attractors, are shown.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Chaos in a single-species discrete population model with stage structure and birth pulses;Advances in Difference Equations;2014-07-18

2. STEADY STATE SYMMETRY BREAKING IN PERIODICALLY EXCITED SYSTEMS INVOLVING TIME DELAY BY HARMONIC HOMOTOPY;International Journal of Bifurcation and Chaos;2013-05

3. Chaotic behavior in a class of delay difference equations;Advances in Difference Equations;2013-04-10

4. Complex dynamics in simple delayed two-parameterized models;Nonlinear Analysis: Real World Applications;2012-12

5. Chaos in a Discrete Delay Population Model;Discrete Dynamics in Nature and Society;2012

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