Geodesic
Periodic solutions of a one-dimensional Wilson-Cowan type model
Electronic journal of differential equations, Tome 2007 (2007)
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__a275,
     author = {Krisner,  Edward P.},
     title = {Periodic solutions of a one-dimensional {Wilson-Cowan} type model},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1135.45006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a275/}
}
TY  - JOUR
AU  - Krisner,  Edward P.
TI  - Periodic solutions of a one-dimensional Wilson-Cowan type model
JO  - Electronic journal of differential equations
PY  - 2007
VL  - 2007
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a275/
LA  - en
ID  - EJDE_2007__2007__a275
ER  - 
%0 Journal Article
%A Krisner,  Edward P.
%T Periodic solutions of a one-dimensional Wilson-Cowan type model
%J Electronic journal of differential equations
%D 2007
%V 2007
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a275/
%G en
%F EJDE_2007__2007__a275
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__a275/