Extending the Concept of Isochrons from Oscillatory to Excitable Systems for Modeling an Excitable Neuron

Abstract

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 excitable systems. The extended isochrons allow reduction of an excitable system described by possibly high dimensional differential equations to a simpler system. We analytically derive a one-dimensional model of an excitable neuron stimulated by instantaneous pulses with the technique of the extended isochrons and show its similarity to an isochronal map numerically obtained from the FitzHugh–Nagumo model. Response characteristics of the one-dimensional model to periodic impulsive stimulations are also analyzed numerically.