High-dimensional memristor-coupled multiple neural networks with spatial multi-structure attractors and application in image encryption

The neurodynamics of the single neural networks with few neurons are extensively studied, but the exploration of the complex neural networks with a large number of neurons, especially for the coupled multiple neural networks and their brain-like chaotic dynamics, are rarely appeared. To this end, this paper constructs a class of high-dimensional memristor-coupled multiple neural networks (HDMMNN) by coupling the different number of sub-Hopfield neural networks through varying the number of memristive synapses. The designed HDMMNN system can help to simulate two or three different brain regions. The theoretical analysis and numerical simulation results show that HDMMNN can generate any desired number of multi-directional multi-structure hyperchaotic attractors, including single direction, grid and spatial multi-structure attractors. Meanwhile, HDMMNN is capable of producing spatial initial-offset coexisting attractors by adjusting the memristor initial values. Furthermore, to verify its physical realizability, HDMMNN is implemented using the FPGA digital hardware platform. Besides, an image encryption scheme with superior security performances is given, which further validates the effectiveness of HDMMNN.