Nonlinear Dynamics

, Volume 62, Issue 1, pp 305–319

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

Original Paper

DOI: 10.1007/s11071-010-9718-2

Cite this article as:
Fan, D., Hong, L. & Wei, J. Nonlinear Dyn (2010) 62: 305. doi:10.1007/s11071-010-9718-2


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.


HR model Time delay Hopf bifurcation Stability switch Periodic solutions 

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.MOE Key Lab for Strength and VibrationXi’an Jiaotong UniversityXi’anP.R. China
  2. 2.Department of MathematicsHarbin Institute of Technology (Weihai)WeihaiP.R. China
  3. 3.Department of MathematicsHarbin Institute of TechnologyHarbinP.R. China

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