Krisner, Edward P.2021-08-132021-08-132007-07-25Krisner, E. P. (2007). Periodic solutions of a one Dimensional Wilson-Cowan type model. <i>Electronic Journal of Differential Equations, 2007</i>(102), pp. 1-22.1072-6691https://hdl.handle.net/10877/14318We 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.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalShootingPeriodicCouplingIntegro-differential equationArticle