Fixed-time projective quasi-synchronization for multi-layer coupled memristive neural networks under deception attacks

This study addresses the issue of fixed-time projective quasi (FTPQ)-synchronization for multi-layer coupled memristive neural networks (MNNs) with deception attacks. Unlike complete synchronization, this paper focuses on the problems of intra-layer synchronization and inter-layer synchronization. A multi-layer coupled MNN model is proposed to characterize not only the multi-layer structures of the network but also the inter-layer and intra-layer interactions among nodes. Deception attackers are assumed to tamper with transmitted information in controller-to-actuator channels, and these attacks are modeled using a Bernoulli random variable. A dynamic event-triggered control (DETC) framework is established to ensure synchronization of multi-layer coupled MNNs, where controller updates only occur when necessary, thereby reducing communication and computation burden. Based on the Lyapunov function method and fixed-time stability theory, sufficient conditions are obtained for both intra-layer and inter-layer FTPQ-synchronization in multi-layer coupled MNNs, while the Zeno phenomena are excluded. Finally, a numerical example with application to image encryption/decryption is presented to validate the obtained results and demonstrate the method’s effectiveness.