Periodic solutions of a one Dimensional Wilson-Cowan type model

Date

2007-07-25

Authors

Krisner, Edward P.

Journal Title

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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.

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Attribution 4.0 International

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