Extending the concept of isochrons from oscillatory to excitable systems for modeling an excitable neuron

In this paper, we study an excitable and nonoscillating neuron on the basis of a technique of extending the concept of isochrons from oscillatory to e xcitable systems. The extended isochrons allow reduction of an excitable sy stem described by possibly high dimensional differential equations to a sim pler system. We analytically derive a one-dimensional model of an excitable neuron stimulated by instantaneous pulses with the technique of the extend ed isochrons and show its similarity to an isochronal map numerically obtai ned from the FitzHugh-Nagumo model. Response characteristics of the one-dim ensional model to periodic impulsive stimulations are also analyzed numeric ally.