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
收藏
页数：14
相关论文
共 50 条
  • [31] Positive periodic solutions of nonautonomous delay competitive systems with weak Allee effect
    Egami, Chikahiro
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (01) : 494 - 505
  • [32] Existence and global attractivity of periodic solution for an impulsive delay differential equation with Allee effect
    Yan, JR
    Zhao, AM
    Yan, WP
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 309 (02) : 489 - 504
  • [33] Permanence and Global Stability of Positive Periodic Solutions of a Discrete Competitive System
    Qin, Wenjie
    Liu, Zhijun
    Chen, Yiping
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2009, 2009
  • [34] Permanence and almost periodic solution of a predator-prey discrete system with Holling IV functional response
    Zhou, Tiejun
    Zhang, Xiaolan
    Xiang, Meihong
    Wu, Zhaohua
    INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2016, 9 (03)
  • [35] Permanence for A Periodic Discrete-time Budworm Population System with Feedback Control
    Yang, Yi
    Liu, Zhijun
    PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 546 - 549
  • [36] On the existence of periodic solution for neutral delay competitive system
    Gui, Zhanji
    Ge, Weigao
    TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (02): : 341 - 355
  • [37] ON THE PERMANENCE FOR n-SPECIES NON-AUTONOMOUS LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH INFINITE DELAYS AND FEEDBACK CONTROLS
    Wang, Kai
    Teng, Zhidong
    Jiang, Haijun
    INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2008, 1 (01) : 29 - 43
  • [38] Permanence in a periodic delay logistic system subject to constant impulsive stocking
    Liu, Zhijun
    Chen, Yiping
    He, Zerong
    Wu, Jianhua
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 33 (08) : 985 - 993
  • [39] Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control
    Xue, Yalong
    Xie, Xiangdong
    Lin, Qifa
    Chen, Fengde
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2018, 2018
  • [40] Almost periodic solution of a discrete competitive system with delays and feedback controls
    Xue, Yalong
    Xie, Xiangdong
    Lin, Qifa
    OPEN MATHEMATICS, 2019, 17 : 120 - 130
12345