Ultimate boundedness for nonautonomous diffusive Lotka-Volterra patches
type: Item
instance of: scholarly article
title: Ultimate boundedness for nonautonomous diffusive Lotka-Volterra patches
zbMATH Open document ID: 0663.92016
DOI: 10.1016/0025-5564(88)90004-1
author: E. Beretta
author: P. Fergola
author: C. Tenneriello
published in: Mathematical Biosciences
publication date: 1988-01-01T00:00:00Z
review text: The asymptotic behavior of n biological species living in two patches is investigated. The governing mathematical model reads as a system of ordinary differential equations of the form \[ \dot x_ i=x_ i[e_ x(t)+A_ x(t)x]_ i+D_ i(t)(y_ i-x_ i),\quad \dot y_ i=y_ i[e_ y(t)+A_ y(t)y]_ i+D_ i(t)(x_ i-y_ i), \] i\(=1,2,...,n\), where \(e_ x,e_ y: {\mathbb{R}}\to {\mathbb{R}}^ n\), \(A_ x,A_ y: {\mathbb{R}}\to R^{n\times n}\), \(x=col(x_ 1,x_ 2,..,x_ n)\), \(y=col(y_ 1,y_ 2,...,y_ n)\). Sufficient conditions which guarantee the ultimate boundedness property of the (positive) solutions are given.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34D40
zbMATH DE Number: 4085479
reviewed by: George Karakostas
MaRDI profile type: Publication
full work available at URL: 0025-5564(88)90004-1
OpenAlex ID: W2040849283
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description: scientific article; zbMATH DE number 4085479