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Bifurcation analysis of a two-dimensional simplified Hodgkin–Huxley model exposed to external electric fields

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Abstract

In this paper, the dynamical behaviors of a two-dimensional simplified Hodgkin–Huxley (H–H) model exposed to external electric fields are investigated through qualitative analysis and numerical simulation. A necessary and sufficient condition is proposed for the existence of the Hopf bifurcation. Saddle-node bifurcations and canards of the simplified model with the coefficients of different linear forms are also discussed. Finally, the bifurcation curves with the coefficients of different linear forms are shown. The numerical results demonstrate that some linear forms can retain the bifurcation characteristics of the original model, which is of great use to simplify the H–H model for the real-world applications.

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Acknowledgments

This work is supported by the National Nature Science Foundation of China under Grant No. 10901014 and No. 61075102, the Science Foundation of Beijing Jiaotong University under Grant 2011JBM130.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, Peoples’ Republic of China

    Hu Wang, Yongguang Yu & Sha Wang

  2. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, Peoples’ Republic of China

    Junzhi Yu

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  1. Hu Wang
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  2. Yongguang Yu
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  3. Sha Wang
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  4. Junzhi Yu
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Correspondence to Yongguang Yu.

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Wang, H., Yu, Y., Wang, S. et al. Bifurcation analysis of a two-dimensional simplified Hodgkin–Huxley model exposed to external electric fields. Neural Comput & Applic 24, 37–44 (2014). https://doi.org/10.1007/s00521-013-1462-3

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  • DOI: https://doi.org/10.1007/s00521-013-1462-3

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