Chaos-hyperchaos transition

The chaos-hyperchaos transition occurs when the second Lyapunov exponent be comes positive. We argue that this transition is mediated by changes in the stability of an infinite number of unstable periodic orbits embedded in th e chaotic attractor. Bifurcations of unstable periodic orbits occur in the neighborhood of the chaos-hyperchaos transition point where we observe unst able variable dimensionality. We give evidence that the chaos-hyperchaos tr ansition is initiated by (i) the saddle-repeller bifurcation of a particula r unstable periodic orbit usually of low period, (ii) the appearance of a r epelling node in the saddle-node bifurcation, after which the chaotic attra ctor becomes riddled, or (iii) the absorption of the repeller (unstable nod e or focus) originally located out of the attractor by the growing attracto r.