Asymptotic stability of pseudo-simple heteroclinic cycles in R^4

Abstract

Robust heteroclinic cycles in equivariant dynamical systems in R^4 have been a subject of intense scientific investigation because, unlike heteroclinic cycles in R^3, they can have an intricate geometric structure and complex asymptotic stability properties that are not yet completely understood. In a recent work, we have compiled an exhaustive list of finite subgroups of O(4) admitting the so-called simple heteroclinic cycles, and have identified a new class which we have called pseudo-simple heteroclinic cycles. By contrast with simple heteroclinic cycles, a pseudo-simple one has at least one equilibrium with an unstable manifold which has dimension 2 due to a symmetry. Here, we analyse the dynamics of nearby trajectories and asymptotic stability of pseudo-simple heteroclinic cycles in R^4.

33 pp., 7 figs., 15 references

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• A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors
• Asymptotic stability of robust heteroclinic networks
• Pseudo-simple heteroclinic cycles in $R^4$
• Robust heteroclinic cycles in pluridimensions