Electron. J. Diff. Eqns., Vol. 2007(2007), No. 102, pp. 1-22.

Periodic 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 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.

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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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