H_∞ Bipartite Synchronization Control of Markov Jump Cooperation–Competition Networks With Reaction–Diffusions

This article is concerned with the bipartite synchronization problem of coupled switching neural networks with cooperative–competitive interactions and reaction–diffusion terms. Different from the existing literature, the networked systems under investigation possess the relationship of cooperation and competition among nodes. Notably, the switching topology is described by a signed graph subject to the Markov jump process with the coexistence of positive and negative interaction weights. Specifically, a positive weight indicates an alliance relationship between two nodes and a negative one shows an adversary relationship. This article aims to design a bipartite synchronization controller for the aforementioned networks with the switching topology such that a prescribed $\mathcal {H}_{\infty }$ bipartite synchronization is satisfied. Then, some sufficient criteria to ensure the stochastic stability of bipartite synchronization error systems are established in view of an appropriate Lyapunov function. Finally, two simulation examples are presented to verify the validity of the proposed bipartite synchronization control method.