A novel hyperchaotic multistable heterogeneous neural network with hidden attractors and its application in image encryption

By simulating the unique properties of different types of neurons and their interconnecting patterns, heterogeneous neural networks can more accurately reflect the structural and functional characteristics of biological neural systems. Therefore, a novel hyperbolic non-volatile locally active memristor is proposed, enabling the construction of a heterogeneous Hindmarsh–Rose neuron memristive synapse-coupled Hopfield neural network (HR-M-HNN) via synaptic characteristic emulation. Dynamic analysis reveals that the HR-M-HNN exhibits hidden attractor characteristics due to the absence of equilibrium points and can generate complex dynamics behaviors, including hyperchaos, chaos, periodic and quasi-periodic, and multistability. Further research reveals a strong correlation between the chaotic state of HR-M-HNN and the locally active control parameter of the memristor. To verify the accuracy of the dynamic analysis, the corresponding analog circuit is designed. Furthermore, based on the HR-M-HNN hyperchaotic system, a novel image encryption scheme is proposed, which utilizes the position index of the Latin square to perform synchronous permutation and diffusion on the plain image, reducing redundant operations and effectively enhancing the encryption speed. Security analyses demonstrate that the proposed image encryption scheme offers excellent performance and robustness.