Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 107, pp. 1-30.

Title: Homoclinic orbit solutions of a one Dimensional
       Wilson-Cowan type model
  
Author: Edward P. Krisner (Univ. of Pittsburgh at Greensburg, PA, USA)
 
Abstract: 
 We analyze a time independent integral equation defined on a
 spatially extended domain which arises in the modelling of neuronal
 networks. In this paper, 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
 N-bump homoclinic orbit solutions for any even-valued N>0.
 homoclinic orbit.
 
Submitted May 14, 2008. Published August 07, 2008.
Math Subject Classifications: 45K05, 92B99, 34C25.
Key Words: Shooting; periodic; coupling; integro-differential equation