Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

Abstract

The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits. This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network (HNN) with coupled hyperbolic memristors through the modification of a single coupling connection weight. The bistable mode of the hyperbolic memristive HNN (mHNN), characterized by the coexistence of asymmetric chaos and periodic attractors, is effectively demonstrated through the utilization of conventional nonlinear analysis techniques. These techniques include bifurcation diagrams, two-parameter maximum Lyapunov exponent plots, local attractor basins, and phase trajectory diagrams. Moreover, an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors. This method demonstrates significant benefits in correlation, information entropy, and resistance to differential attacks, providing strong evidence for its effectiveness in encryption. Additionally, an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN. The correctness of the circuit design is confirmed through Multisim simulations, which align with numerical simulations conducted in Matlab.