Phase Synchronization with Type-II Intermittency in Chaotic Oscillators

Details Phase Synchronization with Type-II Intermittency in Chaotic Oscillators Phase Synchronization with Type-II Intermittency in Chaotic Oscillators

1999-11-30

arxiv.org/abs/chao-dyn/9912003v2

Phy. Rev. E 62, 8826

Nonlinear Sciences

Chaotic Dynamics

5 pages, 5 figures

Scientific paper

10.1103/PhysRevE.62.8826

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 $\epsilon_{c}$ is the PS transition point in coupling strength parameter space), the average length of the time interval between two successive jumps follows $ \sim \exp(\mid\epsilon_{t} - \epsilon\mid^{2})$, which agrees well with the scaling law obtained from the Fokker-Planck equation.

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