2017/07/26 by Adrian C. Murza, Murza, Adrian C.
Mathematics · Medicine · Physics and Astronomy · #34C15 #34D06 #37C80 #37G40 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems #math.DS #msc:34C15 #msc:34D06 #msc:37C80 #msc:37G40
paper · pdf · doi:10.48550/arxiv.1707.08647
8 pages, 1 figure
arxiv created 2017/07/26 · openalex publication_date 2017/07/26 · arxiv updated 2017/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we analyze the heteroclinic cycle and the Hopf bifurcation of a generic dynamical system with the symmetry of the group Q8, constructed via a Cayley graph. While the Hopf bifurcation is similar to that of a D8--equivariant system, our main result comes from analyzing the system under weak coupling. We identify the conditions for heteroclinic cycle between three equilibria in the three--dimensional fixed point subspace of a certain isotropy subgroup of Q8\timesS1. We also analyze the stability of the heteroclinic cycle.