Solving the 2-Dimensional Fokker-Planck Equation for Strongly Correlated Neurons

TL;DR

This paper introduces a novel non-perturbative method to analyze the correlation dynamics of two strongly correlated leaky integrate-and-fire neurons driven by correlated noise, extending beyond linear response limitations.

Contribution

It presents a new non-perturbative approach to solve the 2D Fokker-Planck equation for strongly correlated neuron pairs, generalizing previous linear response models.

Findings

Successfully models both weak and strong correlations

Provides analytical insights into neuronal correlation dynamics

Extends understanding of non-linear neuronal interactions

Abstract

Pairs of neurons in brain networks often share much of the input they receive from other neurons. Due to essential non-linearities of neuronal dynamics, the consequences for the correlation of the output spike trains are not well understood in the strongly correlated regime. Here we consider two leaky integrate-and-fire neurons with correlated white noise input. We analyze this scenario using a novel non-perturbative approach. Hence our treatment covers both weakly and strongly correlated dynamics, generalizing previous results based on linear response theory.