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Stability, symmetry-breaking bifurcations, and chaos in discrete delayed models. (English) Zbl 1147.39301
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.

39A10Additive difference equations
37G40Symmetries, equivariant bifurcation theory
37D45Strange attractors, chaotic dynamics
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