Initial states-induced complex behaviors in a memristive coupled Hopfield neural network model and its application in biomedical image encryption

Abstract The multi-stable memristor is a type of memristor that can store multiple conductance states, optimizing information management and improving the efficiency of artificial neural networks such as Hopfield networks. It can improve the performance of Hopfield neural networks by minimizing the synaptic weight between neurons and increasing information storage capacity through its ability to store multiple levels of conductance. This paper presents and discusses a novel Hopfield neural network model composed of two non-identical sub-neural networks coupled by a flux-controlled multi-stable memristor (MCHNN) and its application in biomedical image encryption. Using analysis methods such as bifurcation diagrams, phase portraits, maximum Lyapunov exponent, and basins of attraction, we analyze the dynamics of the MCHNN model associated with coupling strength and initial states. Numerical results show that the proposed MCHNN model is capable of developing rich and complex dynamics, including chaos, double-bubble bifurcations, homogeneous and non-homogeneous coexisting attractors at different positions induced by initial states. To support the numerical results, the MCHNN model is implemented on a ATmega 2560 microcontroller. The results are in very good agreement with those obtained thoeretically and numerically. We exploit the interesting properties of the proposed MCHNN model to generate random bits for biomedical image encryption. We evaluate the robustness and efficiency of the designed image encryption algorithm by carrying out statistical tests and security analyses.