Pinning synchronization of delayed inertial neural networks with reaction–diffusion terms under stochastic deception attacks using Markov switched control and its application to image encryption

This research delves into the pinning synchronization (PS) of delayed inertial neural networks (DINNs) with reaction–diffusion (RD) terms, under the influence of stochastic deception attacks (DA). By employing Markov switched control strategies, where certain neurons are selected as pinned control nodes, and feedback control inputs are applied at instances of Markov jumps, the dynamics are analyzed. The stochastic DAs are modeled as stochastic impulses, and to tackle this, lemmas concerning the $p$th moment exponential convergence for Markov switched systems are derived based on the uniformly stable function (USF) and the infinitesimal generator of Markov process. These lemmas facilitate the formulation of sufficient criteria for the synchronization of DINNs with RD amidst DA, ensuring mean square convergence. Even if some error systems may diverge under pinning feedback input, ensuring that the pinning feedback controller follows Markov switching can lead the overall error system to achieve mean square convergence. To substantiate the theoretical findings, numerical examples are provided, demonstrating the validity and effectiveness of the proposed synchronization schemes. We propose a novel image encryption scheme that combines DINNs with RD chaotic sequence, introducing a dual confusion mechanism using Knight’s Tour chess scrambling and Hilbert curve transformation. The integration of chaotic sequences with dual confusion enhances encryption strength and security. To validate the cryptosystem, extensive statistical measures, security analyses, and robustness evaluations are performed, demonstrating its efficacy against attacks and practical applicability.