Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 102, pp. 122.
Periodic solutions of a one Dimensional WilsonCowan type model
Edward P. Krisner
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 "heavisidelike" 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
"1bump" periodic solutions.
Submitted May 25, 2007. Published July 25, 2007.
Math Subject Classifications: 45K05, 92B99, 34C25.
Key Words: Shooting; periodic; coupling; integrodifferential equation.
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Edward P. Krisner
B18 Smith Hall
University of Pittsburgh at Greensburg
Greensburg, PA 15601, USA
email: epk15@pitt.edu

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