Pinning synchronization of complex networks via cooperative heterogeneous information

Synchronization is a ubiquitous phenomenon in nature. Over the last two decades, the synchronization of complex networks receives an increasing attention. This paper aims at developing a new pinning synchronization approach for complex networks by using the heterogeneous information of different nodes cooperatively. Heterogeneous information means the different observation of the reference signal. In detail, different from the traditional pinning control idea, this paper utilizes different feedback gains to cope with the corresponding personalized observations of a specific static reference signal for each node to realize network synchronization. Based on our proposed method, this paper obtains three fundamental pinning synchronization theorems with necessary and sufficient conditions for undirected connected networks, strongly connected networks, and networks with a spanning tree, respectively. Following the above theorems, this paper also designs the feedback gains and coupling strength for networks to achieve synchronization. Finally, the numerical simulations are given to validate the proposed approach.