On the structure of phase synchronized chaos

It is well-known that the transition to chaotic phase synchronization for a periodically driven chaotic oscillator of spiral type involves a dense set of saddle-node bifurcations. However, the way of formation and precise organization of these saddle-node bifurcation curves have only recently been examined in detail. By following the development of the phase portrait for the stable and unstable resonance cycles of a forced Rössler system, we demonstrate a variety of processes involved in the formation, reconstruction and final breakdown of complex multi-layered tori. A detailed bifurcation analysis also allows us both to describe the mechanisms that ensure that the regions of existence of the different resonance modes remain bounded and to show how dense sets of saddle-node bifurcations accumulate along the edges of the resonance zone.