Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 107, pp. 130.
Homoclinic orbit 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 modelling of neuronal
networks. In this paper, 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
Nbump homoclinic orbit solutions for any evenvalued N>0.
homoclinic orbit.
Submitted May 14, 2008. Published August 7, 2008.
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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