Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs

Abstract

In this paper, we study finite-time (FET) and fixed-time (FDT) bipartite synchronization of complex networks (CNs) with signed graphs. Under the framework of signed graphs, the interactions between nodes can be either collaborative or antagonistic, which are different from the traditional CNs. Two types of control schemes without the sign function are designed to realize FET and FDT bipartite synchronization of CNs, respectively. By 1-norm analytical techniques and Lyapunov functional method, FET bipartite synchronization criterion is established. By means of the constructed comparison system, FDT bipartite synchronization is proved. In addition, the settling times of both FET synchronization and FDT synchronization are estimated. It is worth noting that the settling time of FDT bipartite synchronization is not related to the initial values. Moreover, numerical simulations are given to illustrate the new results.