Super persistent chaotic transients in physical systems: Effect of noise on phase synchronization of coupled chaotic oscillators

A super persistent chaotic transient is typically induced by an unstable-un stable pair bifurcation in which two unstable periodic orbits of the same p eriod coalesce and disappear as a system parameter is changed through a cri tical value. So far examples illustrating this type of transient chaos util ize discrete-time maps. We present a class of continuous-time dynamical sys tems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2 pi 's in param eter regimes where phase synchronization is expected in the absence of nois e. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We pro vide heuristic arguments for the scaling law of the average transient lifet ime and verify it using numerical examples from both the system of coupled Chua's circuits and that of coupled Rossler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizab le systems.