Stability and Hopf Bifurcation Analysis in Synaptically Coupled FHN Neurons with Two Time Delays

  • Dejun Fan
  • Ling Hong
Conference paper


This chapter presents an investigation of stability and Hopf bifurcation of the synaptically coupled nonidentical FHN neurons with two time delays. By regarding the sum of the two delays as a parameter, it is shown that under certain assumptions, the steady state of the model is absolutely stable; Under another set of conditions, there is a critical value of the parameter, the steady state is stable when the parameter is less than the critical value and unstable when the parameter is greater than the critical value. Thus, oscillations via Hopf bifurcation occur at the steady state when the parameter passes through the critical values. Then, explicit formulas are derived by using the normal form method and center manifold theory to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions.


Periodic Solution Hopf Bifurcation Center Manifold Center Manifold Theory Zero Equilibrium 
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This research is supported by the National Science Foundation of China under Grant No. 10772140 and Harbin Institute Technology (Weihai) Science Foundation with No. HIT(WH)ZB200812.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.MOE Key Laboratory for Strength and Vibration, School of AerospaceXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.Department of MathematicsHarbin Institute of Technology (Weihai)WeihaiPeople’s Republic of China

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