A simple and stable numerical solution for the population density equation.
A population density description of large populations of neurons has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation (PDE). Most of the algorithms proposed to solve this PDE have used finite difference schemes. Here, I use the method of characteristics to reduce the PDE to a set of ordinary differential equations, which are easy to solve. The method is applied to leaky-integrate-and-fire neurons and produces an algorithm that is efficient and yields a stable and manifestly nonnegative density. Contrary to algorithms based directly on finite difference schemes, this algorithm is insensitive to large density gradients, which may occur during evolution of the density.
de Kamps
M
M
Section Cognitive Psychology, Faculty of Social Sciences, Leiden University, 2333 AK Leiden, The Netherlands. kamps@in.tum.de
D000465:Algorithms; D001931:Brain Mapping; D002452:Cell Count; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009434:Neural Pathways; D009474:Neurons / Q000166:cytology*