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

页码：3561 / 3575

页数：15

共 50 条

[41] Hopf bifurcation in a generalized Logistic reaction-diffusion population model with instantaneous and delayed feedback [J].

Yan, Xiang-Ping ;

Zhang, Cun-Hua .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2021, 190 :774-792

[42] The stability and Hopf bifurcation of the diffusive Nicholson's blowflies model in spatially heterogeneous environment [J].

Huang, Dan ;

Chen, Shanshan .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (01)

[43] Global Dynamics of a Kawasaki Disease Vascular Endothelial Cell Injury Model with Backward Bifurcation and Hopf Bifurcation [J].

Guo, Ke ;

Ma, Wan-biao .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2025, 41 (01) :200-233

[44] Hopf bifurcation analysis for a diabetic population model with two delays and saturated treatment [J].

Nasir, Hanis .

PHYSICA SCRIPTA, 2021, 96 (12)

[45] GLOBAL HOPF BIFURCATION OF A POPULATION MODEL WITH STAGE STRUCTURE AND STRONG ALLEE EFFECT [J].

Hao, Pengmiao ;

Wang, Xuechen ;

Wei, Junjie .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2017, 10 (05) :973-993

[46] HOPF BIFURCATION IN AN AGE-DEPENDENT POPULATION MODEL WITH DELAYED BIRTH PROCESS [J].

Bi, Ping ;

Fu, Xianlong .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (06)

[47] Stability and Hopf bifurcation of a diffusive Gompertz population model with nonlocal delay effect [J].

Sun, Xiuli ;

Wang, Luan ;

Tian, Baochuan .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2018, (22)

[48] BISTABLE DYNAMICS AND HOPF BIFURCATION IN A REFINED MODEL OF EARLY STAGE HIV INFECTION [J].

Pankavich, Stephen ;

Neri, Nathan ;

Shutt, Deborah .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (08) :2867-2893

[49] Stability and Hopf bifurcation for a three-component reaction-diffusion population model with delay effect [J].

Ma, Zhan-Ping .

APPLIED MATHEMATICAL MODELLING, 2013, 37 (08) :5984-6007

[50] Spatiotemporal dynamics for a diffusive mussel–algae model near a Hopf bifurcation point [J].

Shihong Zhong ;

Xuehan Cheng ;

Biao Liu .

Advances in Difference Equations, 2021

← 1 2 3 4 5 →