Geodesic
Periodic solutions of a one-dimensional Wilson-Cowan type model
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 45K05, 92B99, 34C25
Keywords: shooting, periodic, coupling, integro-differential equation 
@article{EJDE_2007__2007__a175,
     author = {Krisner, Edward P.},
     title = {Periodic solutions of a one-dimensional {Wilson-Cowan} type model},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a175/}
}
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Krisner, Edward P. Periodic solutions of a one-dimensional Wilson-Cowan type model. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a175/