Analysis of Synchronization in a Neural Population by a Population Density Approach, in "Mathematical Modelling of Natural Phenomena

Abstract. In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two- dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate the phase deviations of a weakly coupled population model. Key words: single neuron model, population density approach, synchronization AMS subject classification: 92C20, 92D25, 34D10, 35L65 1