Phase Jumps near a Phase Synchronization Transition in Systems of Two Coupled Chaotic Oscillators

Abstract

Phase synchronization transitions in two different coupled chaotic systems (R\"ossler and Lorentz) are investigated and shown to be well described by a reduced model of an overdamped periodically driven nonlinear oscillator with a time varying coefficient. In both systems, the phase separation increases with $2\ensuremath{\pi}$ phase jumps below the transition. The scaling rules of the jump near and away from the transition are studied: Near the transition the average interval between two successive jumps follows $\mathrm{ln}〈l〉\ensuremath{\sim}\ensuremath{-}({\ensuremath{\epsilon}}_{c}\ensuremath{-}\ensuremath{\epsilon}{)}^{1/2}$, while away from the transition $〈l〉\ensuremath{\sim}({\ensuremath{\epsilon}}_{t}\ensuremath{-}\ensuremath{\epsilon}{)}^{\ensuremath{-}1/2}$ for both systems.