Periodic solutions of a one Dimensional Wilson-Cowan type model

dc.contributor.authorKrisner, Edward P.
dc.date.accessioned2021-08-13T17:35:37Z
dc.date.available2021-08-13T17:35:37Z
dc.date.issued2007-07-25
dc.description.abstractWe 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.departmentMathematics
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationKrisner, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14318
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectShooting
dc.subjectPeriodic
dc.subjectCoupling
dc.subjectIntegro-differential equation
dc.titlePeriodic solutions of a one Dimensional Wilson-Cowan type modelen_US
dc.typeArticle

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