Coexistence of Multiple Stable States and Bursting Oscillations in a 4D Hopfield Neural Network
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Coexistence of Multiple Stable States and Bursting Oscillations in a 4D Hopfield Neural Network Z. Tabekoueng Njitacke1,2 · J. Kengne2 · H. B. Fotsin3 Received: 23 November 2018 / Revised: 11 December 2019 / Accepted: 12 December 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Neurons are regarded as basic, structural and functional units of the central nerv‑ ous system. They play an active role in the collection, storing and transferring of the information during signal processing in the brain. In this paper, we investigate the dynamics of a model of a 4D autonomous Hopfield neural network (HNN). Our analyses highlight complex phenomena such as chaotic oscillations, periodic win‑ dows, hysteretic dynamics, the coexistence of bifurcations and bursting oscillations. More importantly, it has been found several sets of synaptic weight for which the proposed HNN displays multiple coexisting stable states including three discon‑ nected attractors. Besides the phenomenon of coexistence of attractors, the burst‑ ing phenomenon characterized by homoclinic/Hopf cycle–cycle bursting via homo‑ clinic/fold hysteresis loop is observed. This contribution represents the first case where the later phenomenon (bursting oscillations) occurs in an autonomous HNN. Also, PSpice simulations are used to support the results of the previous analyses. Keywords 4D autonomous HNN · Coexistence of multiple stable states · Bursting oscillations · PSpice simulations
* Z. Tabekoueng Njitacke [email protected] J. Kengne [email protected] H. B. Fotsin [email protected] 1
Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
2
Unité de Recherche d’Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT‑FV Bandjoun, University of Dschang, Bandjoun, Cameroon
3
Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (URMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
Vol.:(0123456789)
Circuits, Systems, and Signal Processing
1 Introduction Hopfield neural network (HNN) was introduced by Hopfield [11]. From then, a bet‑ ter understanding of the dynamical behavior of Hopfield neural networks (HNNs) is of major importance in the study of the information processing and engineering applications [25, 31], such as pattern recognition [25], associative memory and sig‑ nal processing [31]. We recall that HNN is an artificial model obtained from brain dynamics and it is an essential model which plays a substantial role in neurocom‑ puting [37]. Such neuronal model is capable to accumulate some information or specimens in a way similar to the brain. Based on some physiological facts about epilepsy and chaos, Panahi et al. [23] proposed and investigated a model of epilepsy using chaotic artificial neural network. The authors showed that the result of their studies might be helpful to discern epilepsy in a different way and give so
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