The transition to chaotic phase synchronization

Abstract

Abstract. The transition to chaotic phase synchronization for a periodically driven spiral-type chaotic oscillator is known to involve a dense set of saddle-node bifurcations. By following the synchronization transition through the cascade of period-doubling bifurcations in a forced Rössler system, this paper describes how these saddle-node bifurcations arise and how their characteristic cyclic organisation develops. We identify the cycles that are involved in the various saddle-node bifurcations and descibe how the formation of multi-layered resonance cycles in the synchronization domain is related to the torus doubling bifurcations that take place outside this domain. By examining a physiology-based model of the blood Àow regulation to the individual functional unit (nephron) of the kidney we demonstrate how a similar bifurcation structure may arise in this system as a response to a periodically varying arterial blood pressure. The paper ¿nally discusses how an alternative transition to chaotic phase synchronization may occur in the mutual synchronization of two chaotically oscillating period-doubling systems.