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

In weakly coupled systems, it was found that the transition from chaos to hyperchaos occurs after the symmetry-increasing bifurcation. At this bifurcation, the coexisting chaotic attractors located out of the invariant manifold and nonsymmetrical in relation to this manifold merged together, thus creating a chaotic attractor that is symmetrical in relation to the invariant manifold. Both the symmetry-increasing bifurcation and the chaos-hyperchaos transition were found to be caused by bifurcation of an infinite number of unstable periodic orbits.