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

Advances in Difference Equations

Chunling Shi¹  Xiaoying Chen¹  Yiqin Wang² 

[1] College of Zhicheng, Fuzhou University, Fuzhou, P.R. China;Department of Science Research, Fuzhou Fujian Institute of Education, Fuzhou, P.R. China

关键词: Lotka-Volterra system;    discrete delays;    global stability;    extinction;    feedback controls;    34D23;    92D25;    34D20;    34D40;   

DOI  :  10.1186/s13662-017-1410-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY