Firing Patterns and Synchronization of Neuronal Population with Excitatory and Inhibitory Connection

We propose a stochastic model of neuronal population with excitatory and inhibitory connection. We investigate the phase synchrony and firing patterns of a neuronal population by means of Fokker-Planck approach. Numerical simulations show that in a lower excitatory coupling, the presence of inhibitory connection hinders the emergence of synchronous activity in the population, whereas in a stronger coupling, the presence of inhibitory connection facilitates the synchronous activity in the population. Numerical simulations also show that the pattern of firing is low- frequency and regular in a neuronal population without inhibitory connection, but in the presence of inhibitory connection, the pattern of firing becomes stochastic oscillations.