Stationary distributions and cross-correlations in perfect integrate-and-fire models
Our brain is made of a complex network of neurons. In order to get a better understanding of the brains functions we want to focus on the famous Integrate-and-Fire models in particular the perfect one. We want to take a look at two neurons receiving correlated inputs. By extending the perfect integrate-and-fire model through integrating the “fire”-part via a modulo operator we can develop a previously unknown new version of the common model. The aim of this model is to analyze the cross-correlation of two neurons, each driven by a private and a joint Poisson process. Using the stationary distribution of the joint membrane potential, we are able to obtain a closed-form solution for the perfect integrate-and-fire model with only excitatory input. In the model which uses excitatory and inhibitory input signals computational methods fail, but our simulations are successful.