Abstract and Applied Analysis

Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control

Liang Zhao, Xiangdong Xie, Liya Yang, and Fengde Chen

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 867313, 19 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049815

Digital Object Identifier
doi:10.1155/2014/867313

Mathematical Reviews number (MathSciNet)
MR3272221

Zentralblatt MATH identifier
07023224

Citation

Zhao, Liang; Xie, Xiangdong; Yang, Liya; Chen, Fengde. Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control. Abstr. Appl. Anal. 2014 (2014), Article ID 867313, 19 pages. doi:10.1155/2014/867313. https://projecteuclid.org/euclid.aaa/1425049815


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