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Harvest control for a delayed stage-structured diffusive predator–prey model

Xuebing Zhang

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China

Department of Basic Courses, Huaian Vocational College of Information Technology, Huaian 223003, P. R. China

E-mail Address: zxb1030@163.com

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and

Hongyong Zhao

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China

E-mail Address: hyzhao1967@126.com

Corresponding author.

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https://doi.org/10.1142/S1793524517500048Cited by:7 (Source: Crossref)

Abstract

In this paper, we have considered a delayed stage-structured diffusive prey–predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the local stability of an interior equilibrium is established and the existence of Hopf bifurcations at the interior equilibrium is also discussed. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, the complex dynamics are obtained and numerical simulations substantiate the analytical results.

Keywords:

AMSC: 92D25, 70K50, 35B35

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