Two-parameter Hopf-bifurcation of HHM

It is reported that many diseases that are often termed as ion channel disease are related with the aberrance of cell trans-membrane ion channels. This paper took the Hodgkin-Huxley model for muscles as study object, on which the leakage conductance and the sodium ions anti-electromotive force was selected as the parameters to perform the two-parameters Hopf-bifurcation analysis. The influence of bifurcation on the H-H model was also discussed in this paper. With the aid of algebra criterion in high dimension equations, which can be used to prove the existence of Hopf-bifurcation, the task become easier. In addition, this paper also discussed the biological process and tried to prove that the aberrance occurred in the dynamic biological process is accounted for such diseases.