Electron. J. Diff. Eqns., Vol. 2008(2008), No. 107, pp. 1-30.

Homoclinic orbit solutions of a one Dimensional Wilson-Cowan type model

Edward P. Krisner

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 7, 2008.
Math Subject Classifications: 45K05, 92B99, 34C25.
Key Words: Shooting; periodic; coupling; integro-differential equation

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Edward P. Krisner
B-18 Smith Hall
University of Pittsburgh at Greensburg
Greensburg, PA 15601, USA
email: epk15+@pitt.edu

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