Dynamical networks with on-off stochastic connections: Beyond fast switching

We consider networks whose topology changes in time according to a stochastic rule. While the literature gives insight into the effects of fast stochastic connections, little is known about the effects of slower switching on the evolution of a network.We review recent analytical results on convergence properties of fast switching dynamical networks, including bounds on the probability of converging towards an attractor of a multistable network. We also discuss the advantages of slower switching over fast switching, and consider an example in which slow switching provides opportunities for network synchronization while fast switching does not. It is shown that there is an optimal window in which the switching frequency causes an unstable system to stabilize.