Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in ℝ4 R 4

Robust heteroclinic cycles in equivariant dynamical systems in R4 have been a subject of intense scientific investigation because, unlike heteroclinic cycles in R3, 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 analyze the dynamics of nearby trajectories and asymptotic stability of pseudo-simple heteroclinic cycles in R4.