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

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.