Stability and bifurcation analysis of Hodgkin-Huxley model

Hodgkin-Huxley(HH) equation is a classical model in electrophysiology and has been studied by many scholars. Applying stability theory, and taking maximal sodium conductance g̅_na and potassium conductance g̅_k as variables, in this study we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are calculated. When g̅_na is the variable, there is only one bifurcation point and there are two points when g̅_k is variable. The (g̅_na, g̅_k) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when both g̅_na and g̅_k are variables. The results gotten could be a help to control relevant diseases caused by maximal conductance anomaly.