Effects of bias current and control of multistability in 3D hopfield neural network

Bertrand Frederick Boui A Boya; Balamurali Ramakrishnan; Joseph Yves Effa; Jacques Kengne; Karthikeyan Rajagopal

doi:10.1016/j.heliyon.2023.e13034

Effects of bias current and control of multistability in 3D hopfield neural network

Heliyon. 2023 Jan 20;9(2):e13034. doi: 10.1016/j.heliyon.2023.e13034. eCollection 2023 Feb.

Authors

Bertrand Frederick Boui A Boya^{1

2

3}, Balamurali Ramakrishnan⁴, Joseph Yves Effa⁵, Jacques Kengne¹, Karthikeyan Rajagopal⁴

Affiliations

¹ Unité de Recherche d'Automatique et d'Informatique Appliquée (UR-AIA), IUT-FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
² Unité de Recherche de Matière Condensée, d'Electronique et de Traitement Du Signal (UR-MACETS), Department of Physics, University of Dschang, PO Box 67, Dschang, Cameroon.
³ Laboratory of Energy-Electric and Electronic Systems, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon.
⁴ Center for Nonlinear Systems, Chennai Institute of Technology, India.
⁵ Department of Physics, University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon.

Abstract

This work studies the dynamics of a three dimensional Hopfield neural network focusing on the impact of bias terms. In the presence of bias terms, the models displays an odd symmetry and experiences typical behaviors including period doubling, spontaneous symmetry breaking, merging crisis, bursting oscillation, coexisting attractors and coexisting period-doubling reversals as well. Multistability control is investigated by employing the linear augmentation feedback strategy. We numerically prove that the multistable neural system can be adjusted to experience only a single attractor behavior when the coupling coefficient is gradually monitored. Experimental results from a microcontroller based realization of the underlined neural system are consistent with the theoretical analysis.

Keywords: Bias current; Bursting oscillation; Hopfield neural networks; Microcontroller implementation; Multistability control.