Tabekoueng Njitacke Z, Sami Doubla Isaac, Kengne J, Cheukem A
Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon.
Unité de Recherche d'Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon.
Chaos. 2020 Feb;30(2):023101. doi: 10.1063/1.5132280.
In this paper, the effects of asymmetry in an electrical synaptic connection between two neuronal oscillators with a small discrepancy are studied in a 2D Hindmarsh-Rose model. We have found that the introduced model possesses a unique unstable equilibrium point. We equally demonstrate that the asymmetric electrical couplings as well as external stimulus induce the coexistence of bifurcations and multiple firing patterns in the coupled neural oscillators. The coexistence of at least two firing patterns including chaotic and periodic ones for some discrete values of coupling strengths and external stimulus is demonstrated using time series, phase portraits, bifurcation diagrams, maximum Lyapunov exponent graphs, and basins of attraction. The PSpice results with an analog electronic circuit are in good agreement with the results of theoretical analyses. Of most/particular interest, multistability observed in the coupled neuronal model is further controlled based on the linear augmentation scheme. Numerical results show the effectiveness of the control strategy through annihilation of the periodic coexisting firing pattern. For higher values of the coupling strength, only a chaotic firing pattern survives. To the best of the authors' knowledge, the results of this work represent the first report on the phenomenon of coexistence of multiple firing patterns and its control ever present in a 2D Hindmarsh-Rose model connected to another one through an asymmetric electrical coupling and, thus, deserves dissemination.
本文在二维Hindmarsh-Rose模型中研究了两个存在微小差异的神经元振荡器之间电突触连接不对称的影响。我们发现引入的模型具有一个独特的不稳定平衡点。我们同样证明了不对称电耦合以及外部刺激会在耦合神经振荡器中诱发分岔和多种放电模式的共存。利用时间序列、相图、分岔图、最大Lyapunov指数图和吸引子盆，证明了对于某些离散的耦合强度值和外部刺激，至少存在两种放电模式（包括混沌和周期模式）的共存。模拟电子电路的PSpice结果与理论分析结果吻合良好。最特别有趣的是，基于线性增强方案进一步控制了耦合神经元模型中观察到的多稳定性。数值结果表明了通过消除周期性共存放电模式的控制策略的有效性。对于较高的耦合强度值，只有混沌放电模式存在。据作者所知，这项工作的结果代表了关于通过不对称电耦合连接到另一个二维Hindmarsh-Rose模型中多种放电模式共存及其控制现象的首次报道，因此值得传播。
