Windows of opportunity for synchronization in stochastically coupled maps

Highlights: • We study synchronization of stochastically coupled one-dimensional maps. • Non-fast switching conditions are analytically and numerically investigated. • We prove the existence of windows of opportunity for the switching period. • We formulate mathematically-tractable necessary conditions for synchronization. • For tent maps, a closed-form expression for the Lyapunov exponent is derived. Several complex systems across science and engineering display on–off intermittent coupling among their units. Most of the current understanding of synchronization in switching networks relies on the fast switching hypothesis, where the network dynamics evolves at a much faster time scale than the individual units. Recent numerical evidence has demonstrated the existence of windows of opportunity, where synchronization may be induced through non-fast switching. Here, we study synchronization of coupled maps whose coupling gains stochastically switch with an arbitrary switching period. We determine the role of the switching period on synchronization through a detailed analytical treatment of the Lyapunov exponent of the stochastic dynamics. Through closed-form expressions and numerical findings, we demonstrate the emergence of windows of opportunity and elucidate their nontrivial relationship with the stability of synchronization under static coupling. Our results are expected to provide a rigorous basis for understanding the dynamic mechanisms underlying the emergence of windows of opportunity and leverage non-fast switching in the design of evolving networks.