Synchronization and anti-synchronization of multi-layer reaction–diffusion neural networks under bidirectional attacks via a resilient event-triggered mechanism

This paper investigates the synchronization and anti-synchronization problems of multi-layer coupled reaction–diffusion neural networks subject to bidirectional channel attacks. To characterize the cooperative and competitive interactions among nodes in different layers, a signed topology is introduced and the corresponding Laplacian matrix is constructed. By further employing orthogonal transformation techniques, the synchronization and anti-synchronization objectives are reformulated within a unified analytical framework. To reduce communication burden while preserving satisfactory control performance, a resilient adaptive event-triggered control scheme is proposed, which consists of primary and auxiliary controllers. The control phase and control input are updated automatically according to the triggering conditions. In particular, the adaptive triggering threshold is adjusted using not only the current sampled state but also historical sampling information, which enhances the flexibility and resilience of the proposed mechanism under bidirectional channel attacks. By constructing a suitable Lyapunov–Krasovskii functional, sufficient criteria are established to guarantee the desired synchronization and anti-synchronization behaviors of the considered system. Finally, comparative numerical simulations are presented to verify the effectiveness of the proposed method, showing that it achieves strong robustness against bidirectional attacks while maintaining a favorable balance between communication cost and control performance.