Estimation of delay on synchronization stability in a class of complex systems with coupling delays

Nowadays one of the most concerned topics in the field of complex networks is to find how the synchronizability depends on various parameters of networks. Complex networks with coupling delays have gained increasing attention in various fields of science and engineering in the past decade. One interesting problem is to investigate the effect of delay on dynamical behaviors and to determine the range of delay, in which, the synchronization stability can be achieved. In this paper, based on the qualitative theory of linear time-delay systems, the synchronization stability in complex dynamical networks with coupling delays is considered and some stability criteria of synchronization state are obtained. It is shown that by virtue of these obtained criteria, the range of delay on synchronization stability of complex networks with coupling delays can be analytically estimated. Finally, a couple of examples are illustrated which agree well with our theoretical results.