Fixed-Time Projective Synchronization of Multi-Layer Neural Networks in the Presence of Denial-of-Service Attacks

This paper explores the fixed-time projective synchronization of multi-layer neural networks subjected to Denial of Service (DoS) attacks. Different from previous research literatures that focus on the synchronization of single-layer neural networks under network attacks, this work addresses the more practical scenario of multi-layer neural networks, which better reflect real-world conditions. To tackle these challenges, a multi-layer error system under DoS attacks is formulated as a switching system. By leveraging Lyapunov functions and fixed-time stability theory, the paper achieves fixed-time projective synchronization. Numerical simulations are then performed, where each layer in the multi-layer network represents nodes across different layers. The results confirm that synchronization is attained within a predefined settling time, demonstrating rapid convergence and validating the effectiveness of the proposed methodology.