Mathematical analysis of neuronal firing in visual cortex

Abstract

In this article, we discuss the mathematical analysis of neuronal firing in the brain based on the formulation by Sompolinsky (Sompolinsky, Proc. Natl. Acad. Sci., 1990). We first establish a Fokker-Planck equation corresponding to the original stochastic differential equation-based model, then discuss its well-posedness and global-in-time solvability. The asymptotic stability of the incoherence and some properties from the dynamical system aspect are also discussed.