Stability and hopf bifurcation analysis in a stage-structured predator-prey system with two time delays

被引：0
|
作者：
Li, Yongkun [1 ]
Hu, Meng [2 ]
机构：
[1] Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
[2] Department of Mathematics, Anyang Normal University Anyang, Henan 455000, China
来源：
World Academy of Science, Engineering and Technology | 2011年 / 56卷
关键词：
Timing circuits - System stability - Differential equations - Ecosystems - Hopf bifurcation - Predator prey systems;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.
引用
收藏
页码：1504 / 1512
相关论文
共 50 条
  • [21] Stability and bifurcation in a stage-structured predator-prey model with allee effect and time delay
    Xiao, Zaowang
    Li, Zhong
    IAENG International Journal of Applied Mathematics, 2019, 49 (01)
  • [22] Bifurcation insight for a fractional-order stage-structured predator-prey system incorporating mixed time delays
    Xu, Changjin
    Zhang, Wei
    Aouiti, Chaouki
    Liu, Zixin
    Yao, Lingyun
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (08) : 9103 - 9118
  • [23] A Stage-structured Predator-prey Model with Disturbing Pulse and Time Delays
    Cheng, Huidong
    Meng, Xinzhu
    PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 853 - 856
  • [24] A stage-structured predator-prey model with disturbing pulse and time delays
    Song, Xinyu
    Hao, Meiying
    Meng, Xinzhu
    APPLIED MATHEMATICAL MODELLING, 2009, 33 (01) : 211 - 223
  • [25] Hopf bifurcation analysis for a ratio-dependent predator-prey system with two delays and stage structure for the predator
    Deng, Lianwang
    Wang, Xuedi
    Peng, Miao
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 231 : 214 - 230
  • [26] STABILITY AND BIFURCATION OF A STAGE-STRUCTURED PREDATOR-PREY MODEL INCORPORATING A CONSTANT PREY REFUGE
    Zhen Wei
    Haihui Wu
    Changwu Zou
    Annals of Applied Mathematics, 2015, 31 (02) : 212 - 224
  • [27] Role of multiple time delays on a stage-structured predator-prey system in a toxic environment
    Santra, Nirapada
    Saha, Sangeeta
    Samanta, Guruprasad
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 212 : 548 - 583
  • [28] 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
  • [29] Stability and permanence of a delayed stage-structured predator-prey system
    Zou, Ling
    Xiong, Zuoliang
    Wu, Lifeng
    2010 4TH INTERNATIONAL CONFERENCE ON BIOINFORMATICS AND BIOMEDICAL ENGINEERING (ICBBE 2010), 2010,
  • [30] The stability and Hopf bifurcation for a predator-prey system with discrete and distributed delays
    Shu, Zhiping
    Xiong, Zuoliang
    He, Zhifang
    2010 3RD INTERNATIONAL CONFERENCE ON BIOMEDICAL ENGINEERING AND INFORMATICS (BMEI 2010), VOLS 1-7, 2010, : 1277 - 1281
12345