Cascade of torus birth bifurcations and inverse cascade of Shilnikov attractors merging at the threshold of hyperchaos

Abstract

We study the hyperchaos formation scenario in the modified Anishchenko-Astakhov generator. The scenario is connected with the existence of sequence of secondary torus bifurcations of resonant cycles preceding the hyperchaos emergence. This bifurcation cascade leads to the birth of the hierarchy of saddle-focus cycles with a two-dimensional unstable manifold as well as of saddle hyperchaotic sets resulting from the period-doubling cascades of unstable resonant cycles. Hyperchaos is born as a result of an inverse cascade of bifurcations of the emergence of discrete spiral Shilnikov attractors, accompanied by absorbing the cycles constituting this hierarchy.