Antagonistic-information-dependent integral-type event-trigger scheme for bipartite synchronization of cooperative-competitive neural networks and its application

This paper focuses on the bipartite synchronization problem for cooperative-competitive neural networks (CCNNs) by using an antagonistic-information-dependent integral-type event-trigger scheme. Here, the designed antagonistic-information implies that both the cooperation and competition interactions of CCNNs are utilized to design trigger scheme. First, the signed digraph theory, in the presence of structurally balanced topology, is used to describe the antagonistic interactions among neuron nodes. On this basis, such a trigger scheme consisting of antagonistic-information and integral term is proposed to relax communication burden, which can remember the evolution information of CCNNs dynamic process. Meanwhile, the discontinuity of event-triggered scheme can avoid the occurrence of Zeno behavior directly without complicated mathematical analysis. Then, an important lemma is derived to facilitate bipartite synchronization problem. By constructing appropriate Lyapunov function, two novel bipartite synchronization criteria are developed by utilizing the hybrid Lyapunov theories, new lemma, and inequality techniques. At last, an application and an effective example are presented to illustrate the validity and advantage of the proposed method.