A SHORT PROOF FOR HOPF BIFURCATION IN GURTIN-MACCAMY?S POPULATION DYNAMICS MODEL

被引：1
作者：
Ducrot, Arnaud [1 ]
Kang, Hao [1 ,2 ]
Magal, Pierre [3 ,4 ]
机构：
[1] Normandie Univ, UNIHAVRE, LMAH, FR CNRS 3335,ISCN, F-76600 Le Havre, France
[2] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
[3] Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France
[4] CNRS, IMB, UMR 5251, F-33400 Talence, France
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 08期
关键词：
Age structure; population dynamics; Hopf bifurcation; PERIODIC-SOLUTIONS; EQUATIONS; STABILITY;
D O I：
10.1090/proc/15892
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we provide a short proof for the Hopf bifurcation theorem in the Gurtin-MacCamy's population dynamics model. Here we use the Crandall and Rabinowitz's approach, based on the implicit function theo-rem. Compared with previous methods, here we require the age-specific birth rate to be slightly smoother (roughly of bounded variation), but we have a huge gain for the length of the proof.
引用
收藏
页码：3561 / 3575
页数：15
相关论文
共 50 条
  • [21] Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics
    Adimy, M
    Crauste, F
    Ruan, SG
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2005, 6 (04) : 651 - 670
  • [22] Hopf Bifurcation for a Maturity Structured Population Dynamic Model
    Jixun Chu
    Pierre Magal
    Rong Yuan
    Journal of Nonlinear Science, 2011, 21 : 521 - 562
  • [23] Hopf bifurcation of the age-structured SIRS model with the varying population sizes
    Cao, Hui
    Han, Mengmeng
    Bai, Yunxiao
    Zhang, Suxia
    ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (10): : 3811 - 3824
  • [24] Hopf Bifurcation in a Reaction-Diffusion-Advection Population Model with Distributed Delay
    Li, Zhenzhen
    Dai, Binxiang
    Han, Renji
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (16):
  • [25] STABILITY AND HOPF BIFURCATION FOR A CELL POPULATION MODEL WITH STATE-DEPENDENT DELAY
    Adimy, Mostafa
    Crauste, Fabien
    Lhassan Hbid, My
    Qesmi, Redouane
    SIAM JOURNAL ON APPLIED MATHEMATICS, 2010, 70 (05) : 1611 - 1633
  • [26] Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect
    Chen, Shanshan
    Shi, Junping
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (12) : 3440 - 3470
  • [27] Stability and Hopf Bifurcation of a Delayed Viral Infection Dynamics Model with Immune Impairment
    Zhang, Xiaomin
    Xu, Rui
    Song, Chenwei
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (08):
  • [28] Hopf Bifurcation of a Delayed Single Population Model with Patch Structure
    Chen, Shanshan
    Shen, Zuolin
    Wei, Junjie
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2023, 35 (02) : 1457 - 1487
  • [29] A Kind of Hopf Bifurcation of a Population Dynamic Model and its Simulation
    Zhang, Zongjie
    Wei, Xiangqing
    Xu, Shihe
    Li, Kang
    Zhang, Fangwei
    ADVANCED MATERIAL ENGINEERING (AME 2015), 2016, : 91 - 99
  • [30] Hopf Bifurcation of a Delayed Single Population Model with Patch Structure
    Shanshan Chen
    Zuolin Shen
    Junjie Wei
    Journal of Dynamics and Differential Equations, 2023, 35 : 1457 - 1487
12345