María José Cáceres Granados 

A numerical solver for a nonlinear Fokker-Planck equation in Neuroscience 

Due to the huge number of neurons in the visual cortex network a kinetic  approach can be considered. In such a way that the dynamic of the system is analyzed by mean of a distribution function. Therefore, the system of ODEs, which describes the integrate-and-fire models, is replaced  with a system of  PDEs. The advantage of the kinetic models is the reduction of the number of equations and consequently also the time of computation is reduced.  In this talk we show a numerical scheme for the Fokker-Planck system, which models the  visual cortex network dynamics. The deterministic numerical solutions are compared with Monte Carlo simulations. Our numerical solver allows us to obtain the evolution on time of the distribution functions and therefore  the evolution of the macroscopic quantities, since they are moments of the pdf. As a consequence, we validate models which are obtained via moment closures