Mathematics

The talk is concerned with a discrete version of the  Integrate and Fire Model which goes back to Eurich, Hermann and Ernst. I will show how the power law with exponent $-3/2$ of the avalanche size distribution can be derived using an approximation by a branching processes. This result is due to Levina in 2008. The model itself leads to new types of basic mathematical/biological dynamical systems for which  ergodicity will be shown.