Tristability in Model Neurons

The tristability that a class of two-dimensional neuron models may exhibit is investigated in this paper. One proposition and three corollaries on saddles, which play an important role in the dynamics of these models, are proposed and proved using the properties of the Poincare index. Two combinations with three stable states are attained numerically and analyzed geometrically based on INa, p+ IK-model. They are used to interpret visual illusions, and their physiological potentialities and relationship with the short-term memory are discussed.