Local Stability of Synchronization in Complex Networks of Stochastic Dynamical Systems

In this paper, we study the stability properties of complex networks of stochastic dynamical systems. In particular, we extend the Master Stability Function approach to deal with non-deterministic dynamics, and provide necessary and sufficient conditions for the local exponential stability of the synchronization manifold. Our analysis highlights how the noise can be detrimental or beneficial for synchronization depending on the node individual dynamics and on how noise diffuses in the network. The theoretical findings are then illustrated in a set of representative examples.