國立清華大學 數學系

Abstract The Hodgkin-Huxley model (1952) described for the first time how action-potentials in neurons are initiated and propagated. Shortly after HH publication, R. FitzHugh started to study the mathematical properties of the model and decided to program an analogue-computer to solve it. He faced lots of difficulties and, to better understand the mechanism generating spikes, he introduced finally in 1961 a simplified model with only two differential equations called today the FitzHugh-Nagumo model. But he noticed that both HH model and its simplified version show the /all-or-non-principle /or /firing threshold/: there seems to be no smooth increase in action-potential amplitude, but rather a sudden jump in amplitude. In this talk, I will explain how we can understand now this illusion of jump in the light of the canards theory.