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.

中文翻译：

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具有反应扩散的马尔可夫跳跃合作竞争网络的H∞二分同步控制

本文关注具有合作竞争相互作用和反应扩散项的耦合切换神经网络的二分同步问题。与现有文献不同的是，所研究的网络系统具有节点之间的合作与竞争关系。值得注意的是，开关拓扑是通过马尔可夫跳跃过程的符号图来描述的，并且正负交互权重并存。具体来说，正权重表示两个节点之间是联盟关系，负权重表示两个节点之间是敌对关系。本文旨在为上述具有交换拓扑的网络设计一种双向同步控制器，使得规定的 $\mathcal {H}_{\infty }$满足双方同步。然后，考虑到适当的Lyapunov函数，建立了一些充分的准则来保证二分同步误差系统的随机稳定性。最后，给出了两个仿真例子来验证所提出的双向同步控制方法的有效性。