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The Effect of Delay on A Diffusive Predator–Prey System with Modified Leslie–Gower Functional Response

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Abstract

In this paper, a delayed diffusive modified Leslie–Gower-type predator–prey model with Beddington–DeAngelis functional response subject to Neumann boundary condition is considered. The stability/instability of the non-negative equilibria and a detailed Hopf bifurcation analysis are investigated. And explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of normal form and center manifold. In addition, some numerical simulations are carried out.

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Acknowledgments

This research is supported by National Natural Science Foundation of China (Nos. 11031002, 11371111).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People’s Republic of China

    Ruizhi Yang & Junjie Wei

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  1. Ruizhi Yang
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  2. Junjie Wei
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Correspondence to Junjie Wei.

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Communicated by Shangjiang Guo.

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Yang, R., Wei, J. The Effect of Delay on A Diffusive Predator–Prey System with Modified Leslie–Gower Functional Response. Bull. Malays. Math. Sci. Soc. 40, 51–73 (2017). https://doi.org/10.1007/s40840-015-0261-7

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  • DOI: https://doi.org/10.1007/s40840-015-0261-7

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