Hopf bifurcation and heteroclinic cycles in a class of \mathbbD₂-equivariant systems

2014/06/15 by Adrian C. Murza, Murza, Adrian C.
Computer Science · Mathematics · Medicine · #34C15 #34D06 #37C80 #37G40 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #math.DS #msc:34C15 #msc:34D06 #msc:37C80 #msc:37G40

paper · pdf · doi:10.48550/arxiv.1406.3856

13 pages, 2 figures

arxiv created 2014/06/15 · openalex publication_date 2014/06/15 · arxiv updated 2014/06/17 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

In this paper we analyze a generic dynamical system with \mathbbD₂ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from analyzing the system under weak coupling, where we identify the conditions for heteroclinic cycle between four equilibria in the two-dimensional fixed point subspace of some of the isotropy subgroups of \mathbbD₂×\mathbbS¹. We also analyze the stability of the heteroclinic cycle.

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