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 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.