Fixed-time control of competitive complex networks

This paper aims to establish several synchronization criteria of competitive complex networks (CCNs) by using fixed-time (FDT) control. In CCNs, the variations of different nodes are diverse if they are influenced by external environment. Here, we design two types of controller to deal with the different variations of nodes. Meanwhile, these designed controllers guarantee the synchronization of the CCNs in a given time. The estimated settling time improves corresponding results in the literature. Furthermore, based on rigorous mathematical proof and the structured comparison system, several FDT synchronization criteria are obtained. Some comparisons are presented to show the advantages of these new theoretical results. The validity of our theoretical results is illustrated by numerical simulations.