Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks

被引：4
|
作者：
Zhao, Huitao [1 ,2 ]
Sun, Yaowei [1 ]
Wang, Zhen [3 ]
机构：
[1] Zhoukou Normal Univ, Dept Math & Informat Sci, Zhoukou 466001, Henan, Peoples R China
[2] Kunming Univ Sci & Technol, Dept Appl Math, Kunming 650093, Yunnan, Peoples R China
[3] Beifang Univ Nationalities, Inst Informat & Syst Computat Sci, Ningxia 750021, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
关键词：
COMPETITION SYSTEM; STABILITY;
D O I：
10.1155/2014/104156
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard's method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine the directions and stabilities of the bifurcating periodic solutions. We find that these control laws can be applied to control Hopf bifurcation and chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found.
引用
收藏
页数：11
相关论文
共 50 条
  • [1] Stability and bifurcation analysis for a delayed Lotka-Volterra predator-prey system
    Yan, Xiang-Ping
    Chu, Yan-Dong
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 196 (01) : 198 - 210
  • [2] A note on Hopf bifurcations in a delayed diffusive Lotka-Volterra predator-prey system
    Chen, Shanshan
    Shi, Junping
    Wei, Junjie
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (05) : 2240 - 2245
  • [3] Allee Effects in Delayed Lotka-Volterra Predator-Prey System
    Guo, Jianjun
    Li, Weide
    [J]. PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 157 - 161
  • [4] Hopf bifurcation in time-delayed Lotka-Volterra competition systems with advection
    Zhang, Yuanyuan
    [J]. APPLICABLE ANALYSIS, 2019, 98 (09) : 1591 - 1604
  • [5] STABILITY AND HOPF BIFURCATION IN A SYMMETRIC LOTKA-VOLTERRA PREDATOR-PREY SYSTEM WITH DELAYS
    Xia, Jing
    Yu, Zhixian
    Yuan, Rong
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
  • [6] Taylor collocation approach for delayed Lotka-Volterra predator-prey system
    Gokmen, Elcin
    Isik, Osman Rasit
    Sezer, Mehmet
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 268 : 671 - 684
  • [7] Hopf bifurcation in a delayed Lokta-Volterra predator-prey system
    Yan, Xiang-Ping
    Zhang, Cun-Hua
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (01) : 114 - 127
  • [8] Hybrid control of Hopf bifurcation in a Lotka-Volterra predator-prey model with two delays
    Miao Peng
    Zhengdi Zhang
    Xuedi Wang
    [J]. Advances in Difference Equations, 2017
  • [9] Hybrid control of Hopf bifurcation in a Lotka-Volterra predator-prey model with two delays
    Peng, Miao
    Zhang, Zhengdi
    Wang, Xuedi
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,
  • [10] Complexity and chaos control in a discrete-time Lotka-Volterra predator-prey system
    Zhao, Jianglin
    [J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2020, 26 (9-10) : 1303 - 1320
12345