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Zbl 1147.39301
Peng, Mingshu; Yuan, Yuan
Stability, symmetry-breaking bifurcations, and chaos in discrete delayed models. (English)
[J] Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 5, 1477-1501 (2008). ISSN 0218-1274

Summary: 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.

MSC 2000:: *39A10 Difference equations
37G40 Symmetries, equivariant bifurcation theory
37D45 Strange attractors, chaotic dynamics

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