# Linear response in neuronal networks: from neurons dynamics to collective response

## TL;DR

This paper reviews how linear response theory can be explicitly derived for neuronal networks, linking individual neuron dynamics to collective responses using a statistical physics framework.

## Contribution

It introduces a method to derive explicit linear response formulas for neuronal networks based on Gibbs distributions, applicable to different neuron models.

## Key findings

- Explicit formulas for linear response in Amari-Wilson-Cowan model
- Explicit formulas for linear response in conductance-based Integrate and Fire model
- Demonstrates the dependence of network response on parameters

## Abstract

We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitely, including network parameters dependence. This is done in a statistical physics-like approach where one associates to the spontaneous dynamics of the model a natural notion of Gibbs distribution inherited from ergodic theory or stochastic processes. These two examples are the Amari-Wilson-Cowan model and a conductance based Integrate and Fire model.