Phase Synchronization with Type-II Intermittency in Chaotic Oscillators

We study the phase synchronization (PS) with type-II intermittency showing $\pm 2\pi$ irregular phase jumping behavior before the PS transition occurs in a system of two coupled hyperchaotic R"{o}ssler oscillators. The behavior is understood as a stochastic hopping of an overdamped particle in a potential which has $2\pi$-periodic minima. We characterize it as type-II intermittency with external noise through the return map analysis. In $\epsilon_{t} < \epsilon < \epsilon_{c}$(where$\epsilon_{t}$ 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 $<l>\sim \exp (\mid {ϵ}_t-ϵ{\mid }^2)$, which agrees well with the scaling law obtained from the Fokker-Planck equation.