Finite-size dynamics of inhibitory and excitatory interacting spiking neurons.

The dynamic mean-field approach we recently developed is extended to study the dynamics of population emission rates nu (t) for a finite network of coupled excitatory (E) and inhibitory (I) integrate-and-fire (IF) neurons. The power spectrum of nu (t) in an asynchronous state is computed and compared to simulations. We calculate the interpopulations transfer functions and show how synaptic interaction modulates the otherwise low-pass filter with resonances which go well beyond the filter's cut (omega approximately nu) , allowing efficient information transmission on very short time scales determined by spike transmission delays. The saddle-node instability of the asynchronous state is studied and a simple exact dependence of the stability condition on the current-to-rate gain functions is derived, by which self-couplings (EE and II) decrease stability while mutual interaction (EI and IE) favor stability.