A novel extreme multistability system coupled by HR neuron and unidirectional cyclic HNN and its application in medical image encryption

In brain-like research, investigating the impact of heterogeneous neurons on specific neural network structures is of significant importance. In this paper, a heterogeneous memristive synapse-coupled system (HMSCS) is proposed, which is coupled by Hindmarsh–Rose (HR) and unidirectional cyclic Hopfield neural network (HNN), and is established by presenting a new locally active memristor with multi-stable behavior to simulate the synaptic connection between HR neuron and HNN. The dynamic analysis results show that the locally active region of the memristor can significantly affect the chaos range of HMSCS, and the initial value of the memristor can drive a shift in the phase of the attractor, resulting in extreme multistability. In addition, the numerical analyses are validated by circuit design and simulation. Furthermore, a novel medical image encryption scheme is proposed based on the HMSCS chaotic system, in which an improved Hilbert curve permutation method is given, where the traversal direction and starting point of the Hilbert curve are dynamically selected in each round, thereby effectively enhance permutation performance. Additionally, a region-constrained initial value mapping method is proposed to prevent multistability systems from entering periodic orbits due to improper initial value selection, which is a common problem in existing multistability chaotic systems applied to image encryption. Some common security analyses results show that our proposed encryption scheme has excellent security performance for medical image application scenarios.