Cigene Home FUGE logo UMB logo

CIGENE Literature Database

Home |  Show All |  Simple Search |  Advanced Search
1–1 of 1 record found matching your query (RSS): Login
Select All    Deselect All << 1 >> print
  Record Links
Author (up) Oleynik, A.; Wyller, J.; Wertgeim, I. url  openurl
  Title The weakly nonlocal limit of a one-population Wilson-Cowan model Type Journal Article
  Year 2010 Publication Physica D: Nonlinear Phenomena Abbrev Journal  
  Volume 239 Issue 18 Pages 1766-1780  
  Corporate Author Thesis  
  Address  
  Keywords Neural field models; Nonlocal; Wavelet-Galerkin method  
  Abstract We derive the weakly nonlocal limit of a one-population neuronal field model of the Wilson-Cowan type in one spatial dimension. By transforming this equation to an equation in the firing rate variable, it is shown that stationary periodic solutions exist by appealing to a pseudo-potential analysis. The solutions of the full nonlocal equation obey a uniform bound, and the stationary periodic solutions in the weakly nonlocal limit satisfying the same uniform bound are characterized by finite ranges of pseudo energy constants. The time dependent version of the model is reformulated as a Ginzburg-Landau-Khalatnikov type of equation in the firing rate variable where the maximum (minimum) points correspond stable (unstable) homogeneous solutions of the weakly nonlocal limit. Based on this formulation it is also conjectured that the stationary periodic solutions are unstable. We implement a numerical method for the weakly nonlocal limit of the Wilson-Cowan type of model based on the wavelet-Galerkin approach. We perform some numerical tests to illustrate the stability of homogeneous solutions and the evolution of the bumps.  
  Publisher Place Editor  
  Language Summary Language Orig Title  
  Series Editor Series Title Abbrev Series Title  
  Series Volume Series Issue Edition  
  Issn 0167-2789 Isbn Medium  
  Area Expedition Conference  
  Notes Approved no  
  Location Barbara Eriksen (barbara.eriksen@umb.no)  
  Call Number Cigene @ barbara.eriksen @ Serial 1609  
Permanent link to this record
Select All    Deselect All << 1 >> print
Selected Records:    full entries      records per page
      using style:       sort by:  
Home   Search:   Simple  /  Advanced  /  Library Sat, 28 Jan 2012
Help   Tools:   Show Record  /  Extract Citations 03:50:48 +0100