The book aims to provide the tools for analyzing the synchronization of identical systems under time-delayed coupling. On the structural assumption that the system itself is semi-passive — i.e. the system is behaving as a passive system outside some ball-conditions ensuring synchronization of two systems under time-delayed coupling — the framework is extended to the more general situation of a network with time-delayed diffusive coupling. Conditions are derived for time-delay and coupling strength when the network exhibits synchronization or partial synchronization. The theory is illustrated by a number of simulation examples, providing also the experimental results on a network of electronic brain cells.
