Linear Response of General Observables in Spiking Neuronal Network Models

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.

Automated summary

The study establishes a general linear response relation for spiking neuronal networks, predicting the influence of external stimuli on spike correlations and analyzing the impact of memory in spike dynamics on the results. Numerical simulations were conducted using a discrete time integrate and fire model to illustrate the findings.