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Canards dynamics to explore the rhythm transition under electromagnetic induction

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  • Zhan, Feibiao
  • Su, Jianzhong
  • Liu, Shenquan

Abstract

The encoding and transmission of neural information is closely related to neuronal electrophysiological activity such as spike, burst and so on. The main purpose of the paper is to explain the mechanism of transition dynamics between discharge rhythm of mathematical model for neurons under electromagnetic induction. The main dynamical system features involve torus canards. First, the dynamics of spike-burst mode and spiking patterns is demonstrated separately. In addition, the intermediate state spikes of amplitude modulation (AM spike) are found when the spike modes of the neuron are numerically calculated, and the AM mode is illustrated using torus canards. Moreover, the discharge patterns of neuron are compared when considering whether the electromagnetic induction is introduced into the system, and the effect of electromagnetic induction on the discharge rhythm is discussed. Furthermore, the existence regime of the canards phenomenon changes when the system is under the electromagnetic induction, and the dynamics of burst is also different to the original system. Finally, the function of electromagnetic induction on the dynamics of neuron bursts mode, spiking mode and transition mode between burst and spiking is explained.

Suggested Citation

  • Zhan, Feibiao & Su, Jianzhong & Liu, Shenquan, 2023. "Canards dynamics to explore the rhythm transition under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923002059
    DOI: 10.1016/j.chaos.2023.113304
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    References listed on IDEAS

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    1. Slepukhina, Evdokiia & Bashkirtseva, Irina & Ryashko, Lev & Kügler, Philipp, 2022. "Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Baysal, Veli & Yilmaz, Ergin, 2020. "Effects of electromagnetic induction on vibrational resonance in single neurons and neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Zhang, Yin & Wu, Fuqiang & Wang, Chunni & Ma, Jun, 2019. "Stability of target waves in excitable media under electromagnetic induction and radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 519-530.
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    Cited by:

    1. Feibiao Zhan & Yingteng Zhang & Jian Song & Shenquan Liu, 2023. "Canard Mechanism and Rhythm Dynamics of Neuron Models," Mathematics, MDPI, vol. 11(13), pages 1-22, June.

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