Global HOPF bifurcation of a population model with stage structure and strong ALLEE effect

Pengmiao Hao; Xuechen Wang; Junjie Wei

doi:10.3934/dcdss.2017051

Global HOPF bifurcation of a population model with stage structure and strong ALLEE effect

Pengmiao Hao
, Xuechen Wang
, Junjie Wei^*

^*Corresponding author for this work

School of Science

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

This paper is devoted to the study of a single-species population model with stage structure and strong Allee effect. By taking T as a bifurcation parameter, we study the Hopf bifurcation and global existence of periodic solutions using Wu's theory on global Hopf bifurcation for FDEs and the Bendixson criterion for higher dimensional ODEs proposed by Li and Muldowney. Some numerical simulations are presented to illustrate our analytic results using MATLAB and DDE-BIFTOOL. In addition, interesting phenomenon can be observed such as two kinds of bistability.

Original language	English
Pages (from-to)	973-993
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	10
Issue number	5
DOIs	https://doi.org/10.3934/dcdss.2017051
State	Published - Oct 2017

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title = "Global HOPF bifurcation of a population model with stage structure and strong ALLEE effect",

abstract = "This paper is devoted to the study of a single-species population model with stage structure and strong Allee effect. By taking T as a bifurcation parameter, we study the Hopf bifurcation and global existence of periodic solutions using Wu's theory on global Hopf bifurcation for FDEs and the Bendixson criterion for higher dimensional ODEs proposed by Li and Muldowney. Some numerical simulations are presented to illustrate our analytic results using MATLAB and DDE-BIFTOOL. In addition, interesting phenomenon can be observed such as two kinds of bistability.",

author = "Pengmiao Hao and Xuechen Wang and Junjie Wei",

year = "2017",

month = oct,

doi = "10.3934/dcdss.2017051",

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journal = "Discrete and Continuous Dynamical Systems - Series S",

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T1 - Global HOPF bifurcation of a population model with stage structure and strong ALLEE effect

AU - Hao, Pengmiao

AU - Wang, Xuechen

AU - Wei, Junjie

PY - 2017/10

Y1 - 2017/10

N2 - This paper is devoted to the study of a single-species population model with stage structure and strong Allee effect. By taking T as a bifurcation parameter, we study the Hopf bifurcation and global existence of periodic solutions using Wu's theory on global Hopf bifurcation for FDEs and the Bendixson criterion for higher dimensional ODEs proposed by Li and Muldowney. Some numerical simulations are presented to illustrate our analytic results using MATLAB and DDE-BIFTOOL. In addition, interesting phenomenon can be observed such as two kinds of bistability.

AB - This paper is devoted to the study of a single-species population model with stage structure and strong Allee effect. By taking T as a bifurcation parameter, we study the Hopf bifurcation and global existence of periodic solutions using Wu's theory on global Hopf bifurcation for FDEs and the Bendixson criterion for higher dimensional ODEs proposed by Li and Muldowney. Some numerical simulations are presented to illustrate our analytic results using MATLAB and DDE-BIFTOOL. In addition, interesting phenomenon can be observed such as two kinds of bistability.

UR - https://www.scopus.com/pages/publications/85020207410

U2 - 10.3934/dcdss.2017051

DO - 10.3934/dcdss.2017051

M3 - 文章

AN - SCOPUS:85020207410

SN - 1937-1632

VL - 10

SP - 973

EP - 993

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 5

ER -

Global HOPF bifurcation of a population model with stage structure and strong ALLEE effect

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