A master stability function for stochastically coupled chaotic maps

In this paper, we present a master stability function (MSF) for the synchronization of identical maps coupled by a class of stochastically switching weighted directed networks that encompasses Erds-Rényi and numerosity-constrained models. Similarly to the classical MSF for static networks, the stochastic MSF allows for assessing synchronization in terms of spectral properties of the coupling network. Computation of the MSF involves the estimate of the Lyapunov exponents for an auxiliary dynamical system as a function of two independent parameters that are related to the spectral properties of the expectation and autocorrelation of the coupling matrix. We illustrate the results through simulations on chaotic Henon maps coupled through a numerosity-constrained network.