Dynamic behaviors of a discrete Lotka-Volterra competition system with infinite delays and single feedback control
type: Item
instance of: scholarly article
title: Dynamic behaviors of a discrete Lotka-Volterra competition system with infinite delays and single feedback control
zbMATH Open document ID: 1406.92544
DOI: 10.1155/2014/867313
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that if the the discrete Lotka-Volterra competitive system with infinite delays and without feedback control is permanent, then, by choosing some suitable feedback control variable, the permanent species will be driven to extinction. That is, the feedback control variable, which represents the biological control or some harvesting procedure, is the unstable factor of the system. Such a finding overturns the previous scholars' recognition on feedback control variables.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 7023224
zbMATH Keywords: discrete Lotka-Volterra competition system
zbMATH Keywords: feedback control
zbMATH Keywords: infinite delays
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/867313
OpenAlex ID: W2118769155
Wikidata QID: Q59042166
cites work: Stable periodic solution of a discrete periodic Lotka-Volterra competition system
cites work: Permanence in a discrete Lotka-Volterra competition model with deviating arguments
cites work: Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays
cites work: Stable periodic solution of a discrete periodic Lotka-Volterra competition system with a feedback control
cites work: Permanence and global attractivity for discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls
cites work: Permanence of a single species discrete model with feedback control and delay
cites work: Persistence and global stability for discrete models of nonautonomous Lotka-Volterra type.
cites work: Persistence and global stability in discrete models of Lotka--Volterra type
cites work: Extinction in nonautonomous discrete Lotka-Volterra competitive system with pure delays and feedback controls
cites work: On the stability in a discrete two-species competition system
cites work: Extinction in nonautonomous Lotka-Volterra competitive system with pure-delays and feedback controls
cites work: Extinction in a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls
cites work: Note on the persistent property of a discrete Lotka-Volterra competitive system with delays and feedback controls
cites work: Global attractivity of a discrete Lotka-Volterra competition system with infinite delays and feedback controls
cites work: Bifurcation analysis of a two-species competitive discrete model of plankton allelopathy
cites work: The permanence and extinction of a discrete predator-prey system with time delay and feedback controls
cites work: Global stability in \(n\)-dimensional discrete Lotka-Volterra predator-prey models
cites work: Permanence and global attractivity of a discrete two-prey one-predator model with infinite delay
cites work: Feedback control variables have no influence on the permanence of a discrete \(N\)-species cooperation system
cites work: Q4980947
cites work: Global attractivity of almost-periodic solution in a model of hematopoiesis with feedback control
cites work: Permanence for a delayed discrete ratio-dependent predator-prey system with Holling type functional response
cites work: Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model
cites work: Q3424440
cites work: Permanence of species in nonautonomous discrete Lotka-Volterra competitive system with delays and feedback controls
description: scientific article; zbMATH DE number 7023224