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arXiv · 1406.3856

Hopf bifurcation and heteroclinic cycles in a class of $\mathbb{D}_2-$equivariant systems

Adrian C. Murza
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Abstract

In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ 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 $\mathbb{D}_2\times\mathbb{S}^1.$ We also analyze the stability of the heteroclinic cycle.

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Adrian C. Murza. 2014-06-15. Hopf bifurcation and heteroclinic cycles in a class of $\mathbb{D}_2-$equivariant systems. https://arxiv.org/abs/1406.3856

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