Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 102, pp. 1-22.

Title: Periodic solutions of a one Dimensional Wilson-Cowan type model

Author: Edward P. Krisner (Univ. of Pittsburgh, Greensburg, PA, USA)

Abstract:
 We analyze a time independent integral equation defined on a
 spatially extended domain which arises in the modeling of neuronal
 networks. In our survey, the coupling function is oscillatory and
 the firing rate is a smooth "heaviside-like" function.  We will
 derive an associated fourth order ODE and establish that any bounded
 solution of the ODE is also a solution of the integral equation.  We
 will then apply shooting arguments to prove that the ODE has two
 "1-bump" periodic solutions.

Submitted May 25, 2007. Published July 25, 2007.
Math Subject Classifications: 45K05, 92B99, 34C25.
Key Words: Shooting; periodic; coupling; integro-differential equation.