Partial persistence and extinction in \(N\)-dimensional competitive systems
type: Item
instance of: scholarly article
title: Partial persistence and extinction in \(N\)-dimensional competitive systems
zbMATH Open document ID: 1071.34046
author: Shair Ahmad
author: I. M. Stamova
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-22T00:00:00Z
review text: The authors study an N-dimensional system lightly more general than a Lotka-Volterra system. It has the form \[ u_k'(t)=u_k(t)\left[a_k(t)-\sum_{l=1}^N b_{kl}u_l(t)\right],\quad k=1,\dots,N, \] with \(b_{kl}\geq 0,\;b_{kk}>0,\;1\leq k,l,\leq N. \) Conditions for strong persistence of all species are derived. Here, computable conditions are given on the coefficients which imply the ultimate extinction of certain species in an \(N\)-dimensional Lotka-Volterra system.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2136690
zbMATH Keywords: (I,J) conditions
zbMATH Keywords: total persistance
zbMATH Keywords: extinction
zbMATH Keywords: average
zbMATH Keywords: \(N\)-dimensional competitive system
MaRDI profile type: Publication
full work available at URL: j.na.2004.04.013
OpenAlex ID: W2029049217
cites work: Necessary and sufficient average growth in a Lotka–Volterra system
cites work: Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system
cites work: Average growth and total permanence in a competitive Lotka-Volterra System
cites work: Almost necessary and sufficient conditions for survival of species
cites work: Uniformly Persistent Systems
cites work: Persistence in Infinite-Dimensional Systems
cites work: Persistence and extinction in three species Lotka-Volterra competitive systems
cites work: Q3992992
cites work: Permanence and the dynamics of biological systems
cites work: Nonlinear Aspects of Competition Between Three Species
cites work: Kolmogorov vector fields with robustly permanent subsystems
cites work: Lotka-Volterra systems with constant interaction coefficients
cites work: Q4883783
cites work: Q3975200
cites work: Permanence and positive periodic solutions for Kolmogorov competing species systems
DOI: 10.1016/J.NA.2004.04.013
description: scientific article; zbMATH DE number 2136690