Exponential synchronization of directed bipartite networks with node delays and hybrid coupling via impulsive pinning control

Bipartite networks, which comprise two classes of nonoverlapping nodes with links existing only between nodes in different classes, are natural models for many practical systems. Currently, most researches on network synchronization have been focusing on unipartite networks, and relatively few works have been done on bipartite networks. This paper aims to investigate the impulsive pinning control problem for synchronization of directed delayed bipartite networks with node delays and hybrid coupling. By using the methods of average impulsive interval and mathematical induction, some sufficient conditions ensuring global exponential synchronization of the addressed networks are derived. Here, a more flexible impulsive pinning scheme is proposed, which allows the set of pinned nodes as well as the corresponding number of pinned nodes to be different at distinct impulsive instants. Furthermore, an index called impulse pinned proportion is introduced, and the lower bound of impulse pinned proportions is determined, based on which a simple guide to picking what kind of nodes as pinned candidates is given. Some numerical simulations are finally presented to verify the correctness of the derived theoretical results. (c) 2021 Elsevier B.V. All rights reserved.