On synchrony of weakly coupled neurons at low firing rate

The dynamics of a pair of weakly interacting conductance-based neurons, fir ing at low frequency, v, is investigated in the framework of the phase-redu ction 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., inh ibitory) interactions if the synaptic time constant is above a critical val ue tau (c)(s), which scales as \log v\ when v goes to zero.