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.