Pinning synchronization of nonlinearly coupled complex networks with time-varying delays using M-matrix strategies

•The global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays are investigated.•Sufficient conditions are derived for this new class of NCCNs via pinning control by using the M-matrix strategy.•An effective way proposed to adapt the coupling strengths of complex networks.•Numerical examples are given to illustrate the effectiveness of our theoretical results.

In this paper, we investigate the global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays by using an M-matrix approach. The M-matrix strategy allows many synchronization problems with much relaxed conditions to be considered and can be used to derive sufficient conditions for this new class of NCCNs by pinning control. We also propose an effective way of adapting the coupling strengths of complex networks and give numerical examples to illustrate the effectiveness of our theoretical results.