Cluster Synchronization for Multiweighted and Directed Fractional-Order Networks With Cooperative-Competitive Interactions

In this brief, we investigate the cluster synchronization of fractional-order multiweighted complex networks (FOMCNs) via pinning control. Recently, multiweighted complex network has been a hot model to replace classical single-weighted network. The outer coupling matrices (OCMs) are often assumed to be symmetric and strongly connected; moreover, the interactions between nodes are only cooperative. The main contribution of this brief is that we can remove all these limitations, i.e., OCMs can be asymmetric and not connected, while interactions inter-/intra-nodes can be cooperative or competitive. The approach is called re-arranging variables' order technique (ROT), where we combine OCMs with elements in inner linking matrices (ILMs) as coefficients to form union matrices on the same dimension of each node. Some sufficient criteria are presented to guarantee cluster synchronization of FOMCNs, and numerical simulations are given to demonstrate its effectiveness.