Eur. Phys. J. Plus (2022) 137: 841
https://doi.org/10.1140/epjp/s13360-022-03050-6

Regular Article

Memristive bi-neuron Hopfield neural network with coexisting symmetric behaviors

School of Electrical and Automation Engineering, School of Computer and Electronic Information, School of Artificial Intelligence, Nanjing Normal University, 210023, Nanjing, China

^b minfuhong@njnu.edu.cn

Received: 20 April 2022
Accepted: 4 July 2022
Published online: 21 July 2022

Abstract

Memristor is able to describe the electromagnetic induction evoked by membrane potential of neuron. To this end, the paper presents a simple memristive bi-neuron Hopfield neural network (MBHNN) with electromagnetic induction, where a flux-controlled memristor is used to link one neuron directionally. Coexisting symmetric behaviors are uncovered via theoretical analyses, numerical measures, and circuit simulations. By employing theoretical analyses, we demonstrate that the MBHNN model possesses symmetric solutions and symmetric equilibrium points. By utilizing numerical measures including one- and two-argument bifurcation diagrams, dynamical maps, Lyapunov exponent spectra, basins of attraction, and phase plane plots, we confirm that the proposed MBHNN model displays coexisting periodic and chaotic bubbles and coexisting symmetric attractors. In addition, based on the mathematical model, physical analog circuit is built and the corresponding PSIM circuit simulations are deployed to testify these numerically measured results.