Symmetry-increasing bifurcation as a predictor of a chaos-hyperchaos transition in coupled systems

In weakly coupled systems, it is possible to observe the coexistence of the chaotic attractors which are located out of the invariant manifold and are not symmetrical in relation to this manifold. When the control parameter is changed, these attractors can undergo a chaos-hyperchaos transition. We give numerical evidence that before this transition the coexisting attractors merge together creating an attractor symmetrical with respect to the invariant manifold. We argue that the attractors that are not located at the invariant manifold can exhibit dynamical behavior similar to bubbling and on-off intermittency previously observed for the attractors located at the invariant manifold, and we describe the mechanism of these phenomena.