TY - JOUR
AB - Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles.
AU - Flandoli, Franco
AU - Priola, Enrico
AU - Zanco, Giovanni A
ID - 10878
IS - 6
JF - Discrete and Continuous Dynamical Systems
KW - Applied Mathematics
KW - Discrete Mathematics and Combinatorics
KW - Analysis
SN - 1553-5231
TI - A mean-field model with discontinuous coefficients for neurons with spatial interaction
VL - 39
ER -