Transition to Phase Synchronization of Chaos

Abstract

Phase synchronization of chaos is studied using a modified R\"ossler system. By employing a lift of the phase variable (i.e., phase points separated by $2\ensuremath{\pi}$ are not considered as the same), the transition to phase synchronization is viewed as a boundary crisis mediated by an unstable-unstable pair bifurcation on a branched manifold, and the accompanying basin boundary structure is found to be of a new type.