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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

Global Hopf bifurcation of a population model with stage structure and strong Allee effect

Pages: 973 - 993, Volume 10, Issue 5, October 2017      doi:10.3934/dcdss.2017051

 
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Pengmiao Hao - Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China (email)
Xuechen Wang - Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China (email)
Junjie Wei - Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China (email)

Abstract: This paper is devoted to the study of a single-species population model with stage structure and strong Allee effect. By taking $\tau$ 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.

Keywords:  Strong Allee effect, time delay, stage structure, stability, global Hopf bifurcation.
Mathematics Subject Classification:  Primary: 34C23, 34D05; Secondary: 34K28.

Received: July 2016;      Revised: February 2017;      Available Online: June 2017.

 References