Two-parameter bifurcation in a two-dimensional simplified Hodgkin-Huxley model

作者：Wang Hu; Yu Yongguang^*; Zhao Ran; Wang Sha

来源：Communications in Nonlinear Science & Numerical Simulation, 2013, 18(1): 184-193.

DOI：10.1016/j.cnsns.2012.06.022

• Simplified Hodgkin-Huxley model
• Hopf bifurcation
• Canards

The dynamical behaviors of a two-dimensional simplified Hodgkin-Huxley model exposed to external electric fields are investigated based on the qualitative analysis and numerical simulation. A necessary and sufficient condition is given for the existence of the Hopf bifurcation. The stability of equilibrium points and limit cycles is also studied. Moreover, the canards and bifurcation are discussed in the simplified model and original model. The dynamical behaviors of the simplified model are consistent with the original model. It would be a great help to further investigations of the original model.

• 出版日期2013-1
• 单位北京交通大学