Phase Synchronization with Type-II Intermittency in Chaotic Oscillators

Abstract

We study the phase synchronization (PS) with type-II intermittency showing $\pm 2 π$ irregular phase jumping behavior before the PS transition occurs in a system of two coupled hyperchaotic Rössler oscillators. The behavior is understood as a stochastic hopping of an overdamped particle in a potential which has $2 π$-periodic minima. We characterize it as type-II intermittency with external noise through the return map analysis. In $ε_{t} < ε< ε_{c}$ (where $ε_{t}$ is the bifurcation point of type-II intermittency and $ε_{c}$ is the PS transition point in coupling strength parameter space), the average length of the time interval between two successive jumps follows $ \sim \exp(\midε_{t} - ε\mid^{2})$, which agrees well with the scaling law obtained from the Fokker-Planck equation.