  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 rotating in opposite directions
coupled stable heteroclinic cycles 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 appearance and
destruction of chaotic dynamics in the system under study.
