Phase synchronization and crisis in coupled periodically driven chaotic oscillators

Abstract

A nontrivial transition from the synchronous to the nonsynchronous state of two coupled nonautonomous oscillators is studied through the theory of two coupled circle maps (torus maps). For the case of nonidentical systems, the transition occurs without the connection to the change in the sign of Lyapunov exponent. We find that the scaling exponent for the intermittent slips near the critical point, which is measured by rotation sets (fluctuations in rotation vectors), depends on the system parameters unlike the case of phase synchronization for two coupled autonomous chaotic oscillators. We demonstrate that through the model of torus maps this nontrivial transition is induced by a boundary crisis on a torus geometry and intermittent slips could be described as the chaotic transient as a result of the crisis. (C) 2004 Elsevier B.V. All rights reserved.