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, nu, 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 tau(c)(s), which scales as the absolute value of log nu when nu goes to zero.