Abstract
This paper studies the dynamical behaviors of a two-dimensi- onal simplified Hodgkin-Huxley (H-H) model exposed to external electric fields through qualitative analysis and numerical simulation. A necessary and sufficient condition is proposed for the existence of the Hopf bifurcation. Other type of bifurcations 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 real-world applications.
Supported by National Nature Science Foundation of China (10901014, 61075102), and Beijing Jiaotong University Science Foundation (2011JBM130).
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Wang, H., Yu, Y., Wang, S., Yu, J. (2012). Bifurcation Analysis of a Two-Dimensional Simplified Hodgkin-Huxley Model Exposed to External Electric Fields. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34475-6_35
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DOI: https://doi.org/10.1007/978-3-642-34475-6_35
Publisher Name: Springer, Berlin, Heidelberg
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