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–unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems 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 2π’s in parameter regimes where phase synchronization is expected in the absence of noise. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We provide heuristic arguments for the scaling law of the average transient lifetime and verify it using numerical examples from both the system of coupled Chua’s circuits and that of coupled Rössler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizable systems.