Experimental manifestations of phase and lag synchronizations in coupled chaotic systems

Chaotic phase and lag synchronizations are subtle dynamical phenomena in which the phases of two mutually coupled, nonidentical chaotic oscillators become correlated. We investigate to what extent phase and lag synchronizations can be observed in laboratory experiments. Specifically, for phase synchronization, we study the effect of noise. It is found that additive white noise can induce phase slips in integer multiples of 2 pi 's in parameter regimes where phase synchronization is observed in the absence of noise. The average time duration of the temporal phase synchronization scales with the noise amplitude in a way that can be described as super-persistent transient. We give two independent heuristic derivations that yield the same numerically observed scaling law. For lag synchronization, we perform laboratory experiments using chaotic electronic circuits. Our measurements indicate that due to the influence of noise, lag synchronization occurs only intermittently in time. Numerical confirmation and a heuristic explanation to the observed intermittent behavior are given.