Network synchronization through stochastic broadcasting

Synchronization is often observed in interacting dynamical systems, comprising natural, and technological networks; however, seldom do we have precise knowledge and control over the synchronous trajectory. In this letter, we investigate the possibility of controlling the synchronization of a network by broadcasting from a single reference node. We consider the general case in which broadcasting is not static, but stochastically switches in time. Through an analytical treatment of the Lyapunov exponents of the error dynamics between the network and the reference node, we obtain an explicit dependence of synchronization on the strength of the broadcasting signal, the eigenvalues of the network Laplacian matrix, and the switching probabilities of broadcasting. For coupled chaotic tent maps, we demonstrate that: 1) time averaging fails to predict the onset of controlled synchronization and 2) the success of broadcasting depends on the network topology, where the more heterogeneous the network is, the more difficult it is to control.