Synchronization in general complex delayed dynamical networks

This paper investigates synchronization dynamics of a general model of complex delayed networks as well as the effects of time delays. Some simple yet generic criteria ensuring delay-independent and delay-dependent synchronization are derived, which are less conservative than those reported so far in the literature. Moreover, a scale "v" denoted by a function of the smallest and the second largest eigenvalues of coupling matrix is presented to analyze the effects of time delays on synchronization of the networks. Furthermore, various kinds of coupling schemes, including small-world networks and scale-free networks, are studied. It is shown that, if the coupling delays are less than a positive threshold, then the network will be synchronized. On the other hand, with the increase of the coupling delays, the synchronizability of the network will be restrained and even eventually desynchronized. The results are illustrated by a prototype composed of the chaotic Duffing oscillators. Numerical simulations are also given to verify theoretical results.