Bipartite synchronization of delayed competitive-cooperative inertial neural networks: A sign-compensation plus event-triggered controller.

This paper investigates the bipartite synchronization problem of competitive-cooperative inertial neural networks (CCINNs) with time-varying delays under a composite control strategy. The main challenge lies in simultaneously addressing the complex case of non-odd activation functions, inertial dynamics, and multiple time-varying delays, which cannot be resolved by traditional event-triggered control methods. To overcome these limitations, we first transform the system into a manageable coordinate framework using the structural balance condition of signed graphs. Subsequently, a novel composite control strategy is proposed, which integrates a sign-compensation controller (SCC) to eliminate the strict odd-symmetry assumption on activation functions, and an event-triggered controller (ETC) to minimize communication costs. Compared with continuous control, this strategy significantly reduces communication overhead. For theoretical analysis, parameterized system solutions are employed to establish exponential convergence criteria of the error system, avoiding the complexity of traditional Lyapunov functional methods. Finally, a numerical example verifies the effectiveness of the proposed scheme.