Some new results on nonautonomous Lotka-Volterra competitive systems with delays
type: Item
instance of: scholarly article
title: Some new results on nonautonomous Lotka-Volterra competitive systems with delays
zbMATH Open document ID: 0947.34066
author: Yuanhong Yu
author: Zhidong Teng
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-08-28T00:00:00Z
review text: The authors consider the following \(N\)-species nonautonomous Lotka-Volterra type system with finite or infinite delays: \[ \begin{multlined} x_i'(t)= x_i(t)\Bigl[ b_i(t)- a_i(t)x_i (t)-\sum^n_{j=1} a_{ij}(t)x_j \bigl(t- \tau_{ij} (t)\bigr) \\ -\sum^n_{j=1}\int^0_{-\sigma_{ij}} c_{ij}(t,s) x_j (t+s)ds \Bigr], \quad i=1,2, \dots,n.\end{multlined}\tag{1} \] They establish a series of criteria under which a part of the \(n\) species is driven to extinction while the remaining part of the \(n\) species is persistent or uniformly persistent, or coexists globally asymptotically stably. The results in the paper generalize and improve some known results on nondelayed \(N\)-species Lotka-Volterra type competitive systems.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1423862
zbMATH Keywords: nonautonomous Lotka-Volterra system
zbMATH Keywords: delay
zbMATH Keywords: global asymptotical stability
reviewed by: V. Petrov
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6643
OpenAlex ID: W2024417503
cites work: Asymptotically periodic solutions of \(N\)-competing species problem with time delays
cites work: Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay
cites work: Uniform persistence in functional differential equations
cites work: Q4003237
cites work: Q3860165
cites work: Delay differential equations: with applications in population dynamics
cites work: Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria
cites work: Global stability for infinite delay Lotka--Volterra type systems
cites work: Uniform persistence in nonautonomous delay differential Kolmogorov-type population models
cites work: Balancing survival and extinction in nonautonomous competitive Lotka- Volterra systems
cites work: Extinction in nonautonomous competitive Lotka-Volterra systems
cites work: Permanence in Kolmogorov-type systems of nonautonomous functional differential equations
cites work: A nonautonomous model of population growth
cites work: Q4875050
cites work: Global stability of Lotka-Volterra systems with delay
DOI: 10.1006/JMAA.1999.6643
description: scientific article; zbMATH DE number 1423862