Quasi-bipartite synchronization for delayed coupled inertial neural networks having cooperative and competitive communication via pinning control strategy

This study concentrates on achieving quasi-bipartite synchronization within signed coupled inertial neural networks featuring time-varying delays. The pinning controller technique addresses this problem within a structure incorporating cooperative and competitive interaction among the nodes. With the structurally balanced networks, some linear matrix inequality based sufficient conditions are derived for both reduced and non-reduced order methods with the help of Lyapunov–Krasovskii functional to achieve the quasi-bipartite pinning synchronization criterion. Further, the error bound is derived analytically for the leader–follower representation of the signed coupled inertial neural network model. At last, a numerical simulation result is provided to verify the correctness of the established theoretical results.