A Double-Memristor Hopfield Neural Network with Complex Dynamics and Its Application

Abstract

Memristors, known for their unique memory capabilities, are increasingly recognized as key components for the dynamic regulation of neural networks. However, the mechanisms governing multistability and offset-controlled attractors in memristive Hopfield neural networks remain insufficiently understood. To address this gap, this paper conducts a comprehensive dynamical analysis of a novel Hopfield neural network (HNN) in which two distinct memristors are introduced as synaptic connections. The study systematically investigates how adjusting the initial values of the memristors enables precise control of offset-controlled attractors in phase space. Notably, the observed multistability reveals that initial conditions in one dimension can influence oscillatory behaviors in other dimensions. Additionally, an unusual offset-driven attractor-modulation phenomenon is observed in the proposed memristive neural network. To validate these findings, an MCU-based circuit is implemented, confirming the effectiveness of the memristor in managing the network’s dynamics. Furthermore, a security analysis is performed through a pseudo-random number generator (PRNG), demonstrating the robustness of the proposed model in secure communication applications. These results demonstrate the potential of the proposed memristive HNN for secure communication and chaos-based applications.