Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Bertrand Frederick Boui A Boya; Jacques Kengne; Germaine Djuidje Kenmoe; Joseph Yves Effa

doi:10.1016/j.heliyon.2022.e11046

Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Heliyon. 2022 Oct 14;8(10):e11046. doi: 10.1016/j.heliyon.2022.e11046. eCollection 2022 Oct.

Authors

Bertrand Frederick Boui A Boya^{1

2}, Jacques Kengne¹, Germaine Djuidje Kenmoe², Joseph Yves Effa³

Affiliations

¹ Research Unit of Automation and Applied Computer (UR-AIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
² Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé 1, Yaoundé, Cameroon.
³ Department of Physics, University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon.

Abstract

The dynamics of a neural network under several factors (bias current and electromagnetic induction effect) are recently used to simulate activities of the brain under different excitation. In this paper, we introduce a novel Hopfield neural network (HNN) based on two neurons with a memristive synaptic weight connected between neuron one and two based of flux controlled memristor recently proposed by Hua M. et al., in 2022. Using analysis tools, we proved that this model can develop rich dynamical characteristics such as various number of equilibrium points when the parameters are varied, four-scroll attractors, transient chaos, multistability of more than three different attractors and intermittency chaos phenomenon are reported. Moreover, when increasing a synaptic weight, the model shows bursting oscillations phenomenon. To obtain the normal state of the brain, the control of multistability to a strange monostable state is carry out. Finally, microcontroller implementation of the model is considered to verify the numerical analysis.

Keywords: Bursting oscillations; Four-scroll attractor; Hopfield neural network; Microcontroller implementation; Multistability control.