Bifurcations in Morris–Lecar neuron model

The Morris–Lecar (M–L) equations are an important neuron model that exhibits classes I and II excitabilities when system parameters are set appropriately. Although many papers have clarified characteristic behaviors of the model, the detailed transition between two classes is unclear from the viewpoint of bifurcation analyses. In this paper, we investigate bifurcations of invariant sets in a five-dimensional parameter space, and identify an essential parameter of the half-activated potential of the potassium activation curve that contributes to the alternation of the membrane properties of the M–L neuron. We also show that the membrane property can be controlled by varying the value of the single parameter.