Pinning exponential synchronization of coupled neural networks with delay under stochastic deception attacks using the Markov switched control

This topic involves the synchronization of a network of coupled neural networks (CNNs) that have delays in their communication, are subject to stochastic deception (SD) attacks, and are controlled using a pinning Markov switched control strategy. To begin, generalized delayed differential inequality (DDI) with impulses is introduced. The DDI is applied to the next extended delayed impulses stochastically. Which leverages the stochastic properties of the system to enhance robustness against these attacks. By modeling the system under a Markovian switching regime, we develop sufficient conditions for exponential synchronization, taking into account both the network delays and the stochastic characteristics of the deception attacks. Theoretical analysis is conducted using Lyapunov-Krasovskii functionals and stochastic differential equations to derive the stability criteria. The synchronization condition of the coupled NNs with delay under the SD attacks are introduced. Finally, we will present two numerical simulations that demonstrate the validity of our proposed theoretical conclusions. Further explores the application of CNNs with chaotic sequences to enhance image encryption. Using the Hilbert curve and Gingerbread map, we diffuse scrambled images for improved security. The system’s performance is evaluated through differential measurements, demonstrating its robustness.