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Global Hopf bifurcation of a population model with stage structure and strong Allee effect. (English) Zbl 1367.34100

Summary: 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.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
92D25 Population dynamics (general)
34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations

Software:

Matlab; DDE-BIFTOOL
PDFBibTeX XMLCite
Full Text: DOI

References:

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