Chaos in Coupled Heteroclinic Cycles Between Weak Chimeras

Abstract

Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different types of nontrivial dynamics. For instance, as it was shown earlier, chaotic dynamics can appear as a result of interaction via diffusive couplings between two stable heteroclinic cycles between saddle equilibria. We go beyond these findings by considering two coupled stable heteroclinic cycles rotating in opposite directions between weak chimeras. Such an ensemble can be mathematically described by a system of six phase equations. Using two-parameter bifurcation analysis, we investigate the scenarios of emergence and destruction of chaotic dynamics in the system under study.