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Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays

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Abstract

This paper presents an investigation of stability and Hopf bifurcation of a synaptically coupled nonidentical HR model with two time delays. By regarding the half of the sum of two delays as a parameter, we first consider the existence of local Hopf bifurcations, and then derive explicit formulas for determining the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions, using the normal form method and center manifold theory. Finally, numerical simulations are carried out for supporting theoretical analysis results.

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Authors and Affiliations

  1. MOE Key Lab for Strength and Vibration, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Dejun Fan & Ling Hong

  2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, P.R. China

    Dejun Fan & Junjie Wei

  3. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China

    Junjie Wei

Authors
  1. Dejun Fan
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  2. Ling Hong
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  3. Junjie Wei
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Corresponding author

Correspondence to Junjie Wei.

Additional information

This Research is Supported by the National Science Foundation of China (10772140, 10771045) and Harbin Institute of Technology (Weihai) Science Foundation (HIT(WH)ZB200812), and Project Supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2009157).

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Fan, D., Hong, L. & Wei, J. Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays. Nonlinear Dyn 62, 305–319 (2010). https://doi.org/10.1007/s11071-010-9718-2

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  • DOI: https://doi.org/10.1007/s11071-010-9718-2

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