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.

Synchrony in heterogeneous networks of spiking neurons.

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly unstable. We show that at low firing rates, synchrony is more robust in excitatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We introduce a new regime where all inputs, external and internal, are strong and have opposite effects that cancel each other when averaged. In this regime, the robustness of synchrony is strongly enhanced, and robust synchrony can be achieved at a high firing rate in inhibitory networks. On the other hand, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.

On numerical simulations of integrate-and-fire neural networks.

It is shown that very small time steps are required to reproduce correctly the synchronization properties of large networks of integrate-and-fire neurons when the differential system describing their dynamics is integrated with the standard Euler or second-order Runge-Kutta algorithms. The reason for that behavior is analyzed, and a simple improvement of these algorithms is proposed.