Feedback control effect on the Lotka-Volterra prey-predator system with discrete delays

Feedback control effect on the Lotka-Volterra prey-predator system with discrete delays

Abstract In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the br...

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Bibliographic Details
Main Authors: Chunling Shi, Xiaoying Chen, Yiqin Wang
Format: Article
Language:English
Published: SpringerOpen 2017-12-01
Series:Advances in Difference Equations
Subjects:
Lotka-Volterra system
discrete delays
global stability
extinction
feedback controls
Online Access:http://link.springer.com/article/10.1186/s13662-017-1410-0
Description
Summary:Abstract In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback control on predator, the prey species still extinct, whereas the predator species is stable at certain values. Several examples are presented to show the feasibility of the main results.
ISSN:1687-1847

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