The permanence and periodic solution of a competitive system with infinite delay, feedback control, and Allee effect

被引：6

作者：

Shi, Lei ^{[1
]}

Liu, Hua ^{[1
]}

Wei, Yumei ^{[2
]}

Ma, Ming ^{[1
]}

Ye, Jianhua ^{[1
]}

机构：

[1] Northwest Minzu Univ, Sch Math & Comp Sci, Lanzhou, Gansu, Peoples R China

[2] Northwest Minzu Univ, Expt Ctr, Lanzhou, Gansu, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

基金：

中国国家自然科学基金;

关键词：

Permanence; Allee effect; Infinite delay; Feedback control; Periodic solution; LOTKA-VOLTERRA SYSTEM; FUNCTIONAL-DIFFERENTIAL EQUATIONS; GLOBAL ATTRACTIVITY; AVERAGE CONDITIONS; MODEL; EXTINCTION; STABILITY; EXISTENCE;

D O I：

10.1186/s13662-018-1860-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to study the permanence and periodic solution of a competitive system with infinite delay, feedback control, and the Allee effect. We derive sufficient conditions for the permanence and existence of a periodic solution in a competitive system with infinite delay, feedback control, and the Allee effect by using the differential inequality theory and constructing the Lyapunov function. We provide explicit estimates of the lower and upper bounds of the population density. This study reveals that the Allee effect plays an essential role in the permanence and increases the risk of population extinction.

引用

页数：14

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