Vertex-based adaptive synchronization of complex networks

This paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative adaptive strategy. In particular, time-varying feedback coupling gains are considered, whose derivative is made directly dependent on the local synchronization error at each vertex in the network. It is shown that, under appropriate conditions, the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network. The theoretical derivation is complemented by its validation on a set of representative examples.