Robustness of Synchronized Chaotic Oscillations

Abstract

In this paper we address the issue of robustness of synchronized chaotic oscillations in coupled systems. One frequently observes in physical experiments that synchronized chaotic oscillations are occasionally interrupted by brief incidents of unsynchronized behavior. By numerical simulations we show that, under certain circumstances, the regime of synchronized chaos is very sensitive to even small noise and to slightest differences between parameters of coupled systems. As a result of such sensitivity, these small perturbations lead to non-steady, "bursting" synchronization. Using experiments with nonlinear electronic circuits and analytical and numeric analyzes of their ODE model, we study certain bifurcations associated with fixed points and limit cycles in the synchronized chaotic attractor. We establish the connection between these bifurcations and the appearance of the outbursts of unsynchronized behavior. We illustrate a mechanism of formation of complicated invariant sets of trajectories that are associated with the dynamics during such outbursts.