Stochastic synchronization in blinking networks of chaotic maps

Abstract

In this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on-off couplings between any pair of nodes. We focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold. By projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics, we establish a necessary and sufficient condition for stochastic synchronization based on the largest Lyapunov exponent of the map and the spectral radius of such matrix. This condition is further simplified by computing closed-form results for the spectral properties of the moments of the graph Laplacian associated to the intermittent coupling and using classical eigenvalue bounds. We illustrate the main results through simulations on synchronization of chaotic Henon maps.