کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1898764 | 1044772 | 2010 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Some theoretical and numerical results for delayed neural field equations Some theoretical and numerical results for delayed neural field equations](/preview/png/1898764.png)
In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integro-differential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential equations, we show the existence and uniqueness of a solution of these equations. A Lyapunov analysis gives us sufficient conditions for the solutions to be asymptotically stable. We also present a fairly detailed study of the numerical computation of these solutions. This is, to our knowledge, the first time that a serious analysis of the problem of the existence and uniqueness of a solution of these equations has been performed. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our numerical schemes on a variety of examples that are relevant to modeling in neuroscience.
Journal: Physica D: Nonlinear Phenomena - Volume 239, Issue 9, 1 May 2010, Pages 561–578