STABILITY, SYMMETRY-BREAKING BIFURCATIONS AND CHAOS IN DISCRETE DELAYED MODELS-Reference-Cited by-同舟云学术

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

Published:2008-05 Issue:05 Volume:18 Page:1477-1501
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

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)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127408021117

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