Symmetry-Conserving and -Breaking Blow-Out Bifurcations in Coupled Chaotic Systems

We consider blow-out bifurcations of synchronous chaotic attractors on invariant subspaces in coupled chaotic systems with symmetries. Through a blow-out bifurcation, the synchronous chaotic attractor becomes unstable with respect to perturbations transverse to the invariant subspace, and then a new asynchronous chaotic attractor may appear. However, the system symmetry may be preserved or violated when such a transition from synchronous to asynchronous chaotic motion occurs. Here we investigate the underlying mechanism for the symmetry preservation and violation. It is thus found that the shape of a minimal invariant absorbing area controlling the global dynamics and acting as a trapping bounded vessel determines whether the symmetry is conserved or not. For the case of a symmetric absorbing area, a symmetry-conserving blow-out bifurcation occurs while in the case of an asymmetric absorbing area, a symmetry-breaking blow-out bifurcation takes place.