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Bifurcation analysis of a Morris–Lecar neuron model

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Abstract

In this paper, we investigate the dynamical behaviors of a Morris–Lecar neuron model. By using bifurcation methods and numerical simulations, we examine the global structure of bifurcations of the model. Results are summarized in various two-parameter bifurcation diagrams with the stimulating current as the abscissa and the other parameter as the ordinate. We also give the one-parameter bifurcation diagrams and pay much attention to the emergence of periodic solutions and bistability. Different membrane excitability is obtained by bifurcation analysis and frequency-current curves. The alteration of the membrane properties of the Morris–Lecar neurons is discussed.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11172103). The authors are grateful to the referees for their valuable suggestions, which helped us to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Congmin Liu, Xuanliang Liu & Shenquan Liu

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  1. Congmin Liu
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  2. Xuanliang Liu
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  3. Shenquan Liu
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Correspondence to Xuanliang Liu.

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Liu, C., Liu, X. & Liu, S. Bifurcation analysis of a Morris–Lecar neuron model. Biol Cybern 108, 75–84 (2014). https://doi.org/10.1007/s00422-013-0580-4

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  • DOI: https://doi.org/10.1007/s00422-013-0580-4

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