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Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit

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  • Xu, Quan
  • Tan, Xiao
  • Zhu, Dong
  • Bao, Han
  • Hu, Yihua
  • Bao, Bocheng

Abstract

Due to the great importance of the outward current carried by K+ions and the inward one by Na+ and Ca2+ions in 3-D Chay neuron model, the dynamical behaviors associated with the maximal conductances of K+ions channel and mixed Na+-Ca2+ions channel are explored for better demonstrating dynamical effects on the electrical activities in this paper. By utilizing some common dynamical exploring methods, the representative electrical activities of bursting and spiking behaviors endowed with the fast-slow structure of the 3-D Chay neuron model are revealed and classified on the dependence of the two maximal conductances. Moreover, the bifurcation mechanisms for periodic fold/fold bursting, periodic and chaotic fold/homoclinic bursting, and chaotic spiking behaviors are expounded qualitatively by fast-slow dynamical analysis with some specified model parameters. Finally, based on a field programmable gate array (FPGA), a digitally circuit-implemented electronic neuron is made, from which the chaotic and periodic bursting/spiking behaviors are experimentally captured to confirm the numerical simulations.

Suggested Citation

  • Xu, Quan & Tan, Xiao & Zhu, Dong & Bao, Han & Hu, Yihua & Bao, Bocheng, 2020. "Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307487
    DOI: 10.1016/j.chaos.2020.110353
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    6. Yu, Fei & Shen, Hui & Zhang, Zinan & Huang, Yuanyuan & Cai, Shuo & Du, Sichun, 2021. "Dynamics analysis, hardware implementation and engineering applications of novel multi-style attractors in a neural network under electromagnetic radiation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Noel Freddy Fotie Foka & Balamurali Ramakrishnan & André Cheage Chamgoué & Alain Francis Talla & Victor Kamgang Kuetche, 2022. "Neuronal circuit based on Josephson junction actuated by a photocurrent: dynamical analysis and microcontroller implementation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(6), pages 1-8, June.
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    10. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    11. Noel Freddy Fotie Foka & Balamurali Ramakrishnan & André Rodrigue Tchamda & Sifeu Takougang Kingni & Karthikeyan Rajagopal & Victor Kamgang Kuetche, 2021. "Dynamical analysis of Josephson junction neuron model driven by a thermal signal and its digital implementation based on microcontroller," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-7, December.
    12. Ding, Shoukui & Wang, Ning & Bao, Han & Chen, Bei & Wu, Huagan & Xu, Quan, 2023. "Memristor synapse-coupled piecewise-linear simplified Hopfield neural network: Dynamics analysis and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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