Facilitated synchronization of complex networks through a discontinuous coupling strategy

Synchronization stability in complex networks is a topic of theoretical interest and practical importance. Increasing effort has been devoted to the enhancement of synchronizability of networks, or more specifically, the design of synchronizable networks. However, most previous attempts turn the coupling weight/gradient or change the topological interactions, which sometimes is not manageable. In this paper, by adopting a simple kind of discontinuous coupling strategy: the uniform on-off coupling scheme, with on-off period being comparable to the timescale of node dynamics, the problem is solved within the framework of the master stability function. The results show that, this strategy can greatly increase the stable region of synchronization, which means the size of synchronizable networks can be much larger than the traditional case, without any changes of their connections. Furthermore, the synchronization speed can be accelerated considerably, which is even higher than the previous optimal case. The mechanism of the facilitation is revealed and shows that the continuous coupling in fact is one of the worst choices for synchronization in the view of discontinuous coupling strategy. The coupling cost required for synchronization is also examined, which is approximately the same as the continuous coupling