Double integrate-and-fire neuron models coupled via chemical synapses and synchronization phenomena

In this paper, we propose a new type of neuronal firing model, which has some advantages for investigating effects of the firing property on the synchronized behavior. Applying this firing model, synchronous firings in the two models with excitatory or inhibitory synaptic couplings are studied. Then, by analytically constructing a return map of solutions to the Coupled models, conditions for the occurrence of inphase as well as antiphase synchronized oscillations are systematically investigated in terms of parameters demonstrating the firing and synaptic dynamics of the synaptically interconnected models.