Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior

被引：6
|
作者：
Xu, Chaoqun [1 ]
Yuan, Sanling [1 ]
机构：
[1] Shanghai Univ Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
基金：
中国国家自然科学基金;
关键词：
MODIFIED LESLIE-GOWER; PERIODIC-SOLUTIONS; QUALITATIVE-ANALYSIS; MODEL; DYNAMICS;
D O I：
10.1155/2014/568943
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A special predator-prey system is investigated in which the prey population exhibits herd behavior in order to provide a self-defense against predators, while the predator is intermediate and its population shows individualistic behavior. Considering the fact that there always exists a time delay in the conversion of the biomass of prey to that of predator in this system, we obtain a delayed predator-prey model with square root functional response and quadratic mortality. For this model, we mainly investigate the stability of positive equilibrium and the existence of Hopf bifurcation by choosing the time delay as a bifurcation parameter.
引用
收藏
页数：8
相关论文
共 50 条
  • [31] Hopf Bifurcation in a Predator-Prey System with Delays
    Meng, Xinyou
    Huo, Haifeng
    Zhang, Xiaobing
    Xiang, Hong
    PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 228 - 231
  • [32] HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING
    Peng, Miao
    Zhang, Zhengdi
    Wang, Xuedi
    Liu, Xiuyu
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (03): : 982 - 997
  • [33] Hopf Bifurcation of Delayed Predator-prey System with Reserve Area for Prey and in the Presence of Toxicity
    Zhang Zi-zhen
    Chu Yu-gui
    Zhang Xin
    Communications in Mathematical Research, 2018, 34 (02) : 161 - 170
  • [34] Hopf bifurcation analysis in a delayed diffusive predator-prey system with nonlocal competition and schooling behavior
    Zhang, Xiaowen
    Huang, Wufei
    Ma, Jiaxin
    Yang, Ruizhi
    ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (07): : 2510 - 2523
  • [35] Hopf bifurcation in a diffusive predator-prey model with Smith growth rate and herd behavior
    Jiang, Heping
    Fang, Huiping
    Wu, Yongfeng
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [36] Stability and Hopf bifurcation analysis on a delayed Leslie-Gower predator-prey system incorporating a prey refuge
    Li, Yongkun
    Li, Changzhao
    APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (09) : 4576 - 4589
  • [37] Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response
    Xu, Rui
    NONLINEAR DYNAMICS, 2012, 67 (02) : 1683 - 1693
  • [38] Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response
    Rui Xu
    Nonlinear Dynamics, 2012, 67 : 1683 - 1693
  • [39] Stability and Hopf bifurcation in a diffusive predator-prey system with delay effect
    Zuo, Wenjie
    Wei, Junjie
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (04) : 1998 - 2011
  • [40] GLOBAL STABILITY AND HOPF BIFURCATION ON A PREDATOR-PREY SYSTEM WITH DIFFUSION AND DELAYS
    Wang, Yuquan
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2008, 38 (05) : 1685 - 1703
12345