Time delay induced Hopf bifurcation in a diffusive predator-prey model with prey toxicity

被引：5
|
作者：
Yang, Ruizhi [1 ]
Ma, Yuxin [1 ]
Zhang, Chiyu [1 ]
机构：
[1] Northeast Forestry Univ, Dept Math, Harbin 150040, Heilongjiang, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期
关键词：
Predator-prey; Delay; Stability; Hopf bifurcation; SPATIOTEMPORAL PATTERNS; SYSTEM; DYNAMICS;
D O I：
10.1186/s13662-020-03161-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a diffusive predator-prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining the property of Hopf bifurcation are given.
引用
收藏
页数：17
相关论文
共 50 条
  • [1] Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity
    Ruizhi Yang
    Yuxin Ma
    Chiyu Zhang
    [J]. Advances in Difference Equations, 2021
  • [2] Hopf bifurcation of a predator-prey model with time delay and stage structure for the prey
    Li Feng
    Li Hongwei
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2012, 55 (3-4) : 672 - 679
  • [3] Hopf bifurcation and optimal control in a diffusive predator-prey system with time delay and prey harvesting
    Chang, Xiaoyuan
    Wei, Junjie
    [J]. NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2012, 17 (04): : 379 - 409
  • [4] Stability and Hopf bifurcation of a predator-prey model with stage structure and time delay for the prey
    Song, Yan
    Xiao, Wen
    Qi, Xiaoyu
    [J]. NONLINEAR DYNAMICS, 2016, 83 (03) : 1409 - 1418
  • [5] HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND PREY HARVESTING
    Jiang, Heping
    Tang, Xiaosong
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (02): : 671 - 690
  • [6] Stability and Hopf bifurcation in a diffusive predator-prey system with delay effect
    Zuo, Wenjie
    Wei, Junjie
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (04) : 1998 - 2011
  • [7] Hopf bifurcation in a diffusive predator-prey model with competitive interference
    Liu, Fuxiang
    Yang, Ruizhi
    Tang, Leiyu
    [J]. CHAOS SOLITONS & FRACTALS, 2019, 120 : 250 - 258
  • [8] Hopf bifurcation in a diffusive predator-prey model with group defence
    Ruan, SG
    Wei, JJ
    Xiao, DM
    [J]. ADVANCED TOPICS IN BIOMATHEMATICS, 1998, : 219 - 227
  • [9] Stationary pattern and Hopf bifurcation of a diffusive predator-prey model
    Fan, Xiuzhen
    Zhou, Feng
    Li, Yan
    [J]. APPLICABLE ANALYSIS, 2023, 102 (08) : 2141 - 2159
  • [10] Hopf bifurcation analysis in a predator-prey model with predator-age structure and predator-prey reaction time delay
    Zhang, Xiangming
    Liu, Zhihua
    [J]. APPLIED MATHEMATICAL MODELLING, 2021, 91 : 530 - 548
12345