Dynamic analysis of spatial multi-structure Hopfield neural networks with extreme multi-stable homogeneous attractors based on ISRU memristor coupling

Memristors with their inherent nonlinear and memory properties have demonstrated significant potential in constructing neural networks with highly complex dynamic behaviors and highly biomimetic neural network models. This paper proposes a model based on the inverse square root function (ISRU) for multistable memristor and conducts an in-depth analysis of the inherent characteristics and multi-stable behavior of this type of memristor. By replacing the self-synaptic weights in the Hopfield neural network with the memristors, a multi-stable memristor coupled Hopfield neural network chaotic system is constructed. The dynamical analysis shows that the IMMHNN system can generate multi-dimensional attractors that are arbitrarily controlled through parameter regulation and achieve the coexistence of multi-dimensional space attractors controlled by initial values. To verify the physical realizability of the system, an equivalent circuit of the IMMHNN was designed based on the Multisim platform and simulation verification was conducted. Finally, leveraging the complex dynamical characteristics of the IMMHNN, a satellite remote sensing image encryption scheme was proposed. This scheme integrates its chaotic sequence, a DCT-based frequency domain encryption algorithm and an affine transformation. The experiment results show that the scheme has both high efficiency and high security.