Synchronization Probability in Large Complex Networks

In a generalized framework, where multistate and interstate linkages are allowed, the synchronization of oscillators in random networks is investigated. A sufficient condition for the stability of synchronization is derived, which explicitly relates the network structure and the local and coupling dynamics to synchronization stability. This condition is then translated into a lower bound on the probability of stability of synchrony for large Erdös-Rényi and Newman-Watts small-world networks.