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Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation
Chaos, Solitons & Fractals ( IF 7.8 ) Pub Date : 2020-05-16 , DOI: 10.1016/j.chaos.2020.109785
Zeric Tabekoueng Njitacke , Isaac Sami Doubla , Sandrine Mabekou , Jacques Kengne

In this paper, the effects of a threshold electromagnetic induction, as well as an asymmetry in the electrical synaptic coupling between two neuronal oscillators, are studied through a 2D Hindmarsh-Rose model. We have found that the introduced model has no-equilibrium point and thus, displays hidden dynamics. We equally demonstrate that the electromagnetic induction strength combined with an asymmetric electrical coupling and external stimulus induces 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 the electromagnetic induction strength, coupling strengths, and external stimulus is demonstrated using time series, phase portraits, bifurcation diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The PSpice results with analog electronic circuits are in good agreement with the results of theoretical analyses. To the best of the author's knowledge, the results of this work represent the first report on the phenomenon of coexistence of multiple firing patterns in a coupled 2D Hindmarsh-Rose model under threshold electromagnetic induction effect thus, deserve dissemination.



中文翻译:

与不对称电耦合相连接的两个神经元的隐性电活动受到电磁感应:模式的共存及其模拟实现

在本文中,通过二维Hindmarsh-Rose模型研究了阈值电磁感应的影响以及两个神经元振荡器之间电突触耦合的不对称性。我们发现,引入的模型没有平衡点,因此显示了隐藏的动力学。我们同样证明,电磁感应强度与不对称的电耦合和外部刺激相结合,会在耦合的神经振荡器中引起分叉和多种激发模式的共存。使用时间序列,相图,分叉图,最大李雅普诺夫指数图,和吸引盆地。模拟电子电路的PSpice结果与理论分析的结果非常吻合。据作者所知,这项工作的结果代表了在阈值电磁感应作用下耦合二维Hindmarsh-Rose模型中多个点火模式共存现象的首次报道,因此值得推广。

更新日期:2020-05-16
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