Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling

We study synchronization in an array of coupled nonlinear systems with delay and nonreciprocal time-varying coupling and present synchronization criteria which generalize previous synchronization results. We show that the array synchronizes when the nondelay coupling term is cooperative and large enough. Furthermore, we show that the synchronization criteria are related to several matrix quantities describing the coupling topology. These quantities can be considered as generalizations of the concept of algebraic connectivity to directed graphs. Index Terms--Delay systems, directed graphs, Lyapunov methods, nonlinear systems, synchronization.