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 $\nu \left(t\right)$ for a finite network of coupled excitatory $\left(E\right)$ and inhibitory $\left(I\right)$ integrate-and-fire (IF) neurons. The power spectrum of $\nu \left(t\right)$ 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 $(\omega \sim \nu )$, 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.