Periodic solutions of a one Dimensional Wilson-Cowan type model
Date
2007-07-25
Authors
Krisner, Edward P.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Shooting, Periodic, Coupling, Integro-differential equation
Citation
Krisner, 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.
Rights
Attribution 4.0 International