On Synchrony of Weakly Coupled Neurons at Low Firing Rate

The dynamics of a pair of weakly interacting conductance-based neurons, firing at low frequency, v, is investigated in the framework of the phase-reduction method. The stability of the antiphase and the in-phase locked state is studied. It is found that for a large class of conductance-based models, the antiphase state is stable (resp., unstable) for excitatory (resp., inhibitory) interactions if the synaptic time constant is above a critical value τ^c_s, which scales as |logv| when v goes to zero.