Permanence for a large class of planar periodic Kolmogorov systems
type: Item
instance of: scholarly article
title: Permanence for a large class of planar periodic Kolmogorov systems
zbMATH Open document ID: 1004.34032
author: Bertha Granados
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-04T00:00:00Z
review text: The author deals with a large class of planar periodic Kolmogorov systems \[ \dot x(t)= x(t)f(t, x(t),y(t)),\qquad \dot y(t)= y(t)g(t,x(t),y(t)), \] where \(f,g: \mathbb{R}\times \mathbb{R}_+^2\rightarrow \mathbb{R}\) are continuous functions which are locally Lipschitz continuous in \((x, y)\) and \(T\)-periodic in time \(t\), for some \(T>0\). Here, the author proves that the periodic Kolmogorov system (including competition, mutualism, and some classes of predator-prey systems) is permanent when the subsystems of single species have a positive global attractive periodic solution and satisfy some additional conditions. Some results in the literature are extended and completed.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1763483
zbMATH Keywords: permanence
zbMATH Keywords: positive periodic solution
zbMATH Keywords: Kolmogorov systems
reviewed by: Lansun Chen
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7080
OpenAlex ID: W2005202017
cites work: Permanence for non-autonomous predator-prey systems
cites work: Predator-prey models with almost periodic coefficients
cites work: Q3992992
cites work: An iterative scheme for the \(N\)-competing species problem
cites work: Permanence of a large class of periodic predator-prey systems
cites work: Permanence and positive periodic solutions for Kolmogorov competing species systems
DOI: 10.1006/JMAA.2000.7080
description: scientific article; zbMATH DE number 1763483