Spiking neuron models with excitatory or inhibitory synaptic couplings and synchronization phenomena

We investigate synchronization phenomena in a system of two piecewise-linear-type model neurons with excitatory or inhibitory synaptic couplings. Employing the phase plane analysis and a singular perturbation approach to split the dynamics into slow and fast ones, we construct analytically the Poincaré map of the solution to the piecewise-linear equations. We investigate conditions for the occurrence of synchronized oscillations of in phase as well as of antiphase in terms of parameters representing the strength of the synaptic coupling and the decaying relaxation rate of the synaptic dynamics. We present the results of numerical simulations that agree with our theoretical ones.