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