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.
References