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Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field

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Abstract

Models of neurons play an essential role in computational neuroscience. They provide a virtual laboratory to analyze the different regimes in the electrical activities of a single neuron or a network of neurons. They help the neuroscientist to have a better look at the nervous system. Some researchers have claimed that the transition of the ions through the membrane may induce an electrical field. In this paper, a new neuronal model is investigated which considers the effect of the electrical field. The dynamical properties of this model are studied. Different dynamical analyses are carried out to this end: investigating the stability of the equilibria, observing state space and trajectories, obtaining bifurcation diagram and Lyapunov exponents’ diagram, and finally exploring the basin of attraction.

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Acknowledgements

This work is supported by the Hunan Provincial Department of Education General Project Fund (No. B08004056) and the National Natural Science Foundation of China (Grant Nos. 61901530, 11747150).

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Shaoyang University, Shaoyang, 422000, China

    Bo Yan

  2. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    Shirin Panahi

  3. School of Physics and Electronics, Central South University, Changsha, 410083, China

    Shaobo He

  4. Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran, 159163-4311, Iran

    Sajad Jafari

  5. Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran, 159163-4311, Iran

    Sajad Jafari

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  1. Bo Yan
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  2. Shirin Panahi
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Correspondence to Sajad Jafari.

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Yan, B., Panahi, S., He, S. et al. Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field. Nonlinear Dyn 101, 521–529 (2020). https://doi.org/10.1007/s11071-020-05816-y

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  • DOI: https://doi.org/10.1007/s11071-020-05816-y

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