Theoretical analysis of synchronization in delayed complex dynamical networks with discontinuous coupling

In this paper, we study the synchronization problem of time-delayed complex networks with discontinuous coupling. Sufficient conditions for the synchronization are obtained based on the stability theory of differential equations. The theoretical results show that the time-delayed networks can achieve synchronization even if the coupling is switched off sometimes. We find analytically that the speed of synchronization is proportional to the on–off rate of the coupling and the algebraic connectivity of networks. Finally, the analytical results are confirmed by numerical simulations.