Periodic solutions of a one Dimensional Wilson-Cowan type model
| dc.contributor.author | Krisner, Edward P. | |
| dc.date.accessioned | 2021-08-13T17:35:37Z | |
| dc.date.available | 2021-08-13T17:35:37Z | |
| dc.date.issued | 2007-07-25 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Krisner, E. P. (2007). Periodic solutions of a one Dimensional Wilson-Cowan type model. Electronic Journal of Differential Equations, 2007(102), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14318 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Shooting | |
| dc.subject | Periodic | |
| dc.subject | Coupling | |
| dc.subject | Integro-differential equation | |
| dc.title | Periodic solutions of a one Dimensional Wilson-Cowan type model | en_US |
| dc.type | Article |