A Density Model for a Population of Theta Neurons

Abstract

Abstract Population density models that are used to describe the evolution of neural populations in a phase space are closely related to the single neuron model that describes the individual trajectories of the neurons of the population and which give in particular the phase-space where the computations are made. Based on a transformation of the quadratic integrate and fire single neuron model, the so-called theta-neuron model is obtained and we shall introduce in this paper a corresponding population density model for it. Existence and uniqueness of a solution will be proved and some numerical simulations are presented. The results of existence are compared to previous results of existence or nonexistence (burst) for populations of leaky integrate and fire neurons.