A necessary and sufficient condition for global asymptotic stability of time-varying Lotka-Volterra predator-prey systems
type: Item
instance of: scholarly article
title: A necessary and sufficient condition for global asymptotic stability of time-varying Lotka-Volterra predator-prey systems
zbMATH Open document ID: 1328.34046
author: Jitsuro Sugie
author: Wei Zheng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2015-09-30T00:00:00Z
review text: The authors consider the time-varying Lotka-Volterra predator-prey system \[ \frac{dN}{dt}=(a+ch(t)-dh(t)N-bP)N,\quad \frac{dP}{dt}=(-c+dN)P,\eqno(E) \] \(N\) and \(P\) represent the prey population (or density) and the predator population (or density), respectively; the function \(h(t)\) is nonnegative, and \(a,b,c\) and \(d\) are positive constants. Necessary and sufficient conditions for the global asymptotic stability of the unique interior equilibrium \(x^*=(c/d, a/b)\) have been obtained in this paper.
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 6487756
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: Lotka-Volterra predator-prey model
zbMATH Keywords: time-varying system
reviewed by: Alexander O. Ignatyev
MaRDI profile type: Publication
full work available at URL: j.na.2015.06.031
OpenAlex ID: W1560902876
cites work: Q5569709
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Wikidata QID: Q115568784
DOI: 10.1016/J.NA.2015.06.031
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description: scientific article; zbMATH DE number 6487756