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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

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  • Njitacke, Zeric Tabekoueng
  • Doubla, Isaac Sami
  • Mabekou, Sandrine
  • Kengne, Jacques

Abstract

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.

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  • Njitacke, Zeric Tabekoueng & Doubla, Isaac Sami & Mabekou, Sandrine & Kengne, Jacques, 2020. "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, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920301879
    DOI: 10.1016/j.chaos.2020.109785
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    References listed on IDEAS

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    6. Kengne, Jacques & Mogue, Ruth Line Tagne & Fozin, Theophile Fonzin & Telem, Adelaide Nicole Kengnou, 2019. "Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 63-84.
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    Cited by:

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    2. Chen, Xiongjian & Wang, Ning & Wang, Yiteng & Wu, Huagan & Xu, Quan, 2023. "Memristor initial-offset boosting and its bifurcation mechanism in a memristive FitzHugh-Nagumo neuron model with hidden dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Bao, Bocheng & Chen, Liuhui & Bao, Han & Chen, Mo & Xu, Quan, 2024. "Bifurcations to bursting oscillations in memristor-based FitzHugh-Nagumo circuit," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Fossi, Jules Tagne & Njitacke, Zeric Tabekoueng & Tankeu, William Nguimeya & Mendimi, Joseph Marie & Awrejcewicz, Jan & Atangana, Jacques, 2023. "Phase synchronization and coexisting attractors in a model of three different neurons coupled via hybrid synapses," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. Tabekoueng Njitacke, Zeric & Tsafack, Nestor & Ramakrishnan, Balamurali & Rajagopal, Kartikeyan & Kengne, Jacques & Awrejcewicz, Jan, 2021. "Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    6. Shadizadeh, S. Mohadeseh & Nazarimehr, Fahimeh & Jafari, Sajad & Rajagopal, Karthikeyan, 2022. "Investigating different synaptic connections of the Chay neuron model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    7. Njitacke, Zeric Tabekoueng & Ramakrishnan, Balamurali & Rajagopal, Karthikeyan & Fonzin Fozin, Théophile & Awrejcewicz, Jan, 2022. "Extremely rich dynamics of coupled heterogeneous neurons through a Josephson junction synapse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    8. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    9. Leng, Xiangxin & Gu, Shuangquan & Peng, Qiqi & Du, Baoxiang, 2021. "Study on a four-dimensional fractional-order system with dissipative and conservative properties," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Jules Tagne Fossi & Vandi Deli & Hélène Carole Edima & Zeric Tabekoueng Njitacke & Florent Feudjio Kemwoue & Jacques Atangana, 2022. "Phase synchronization between two thermo-photoelectric neurons coupled through a Josephson Junction," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(4), pages 1-17, April.

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