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Dynamics in a diffusive modified Leslie–Gower predator–prey model with time delay and prey harvesting

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Abstract

The dynamics of a diffusive predator–prey model with time delay and Michaelis–Menten-type harvesting subject to Neumann boundary condition is considered. Turing instability and Hopf bifurcation at positive equilibrium for the system without delay are investigated. Time delay-induced instability and Hopf bifurcation are also discussed. By the theory of normal form and center manifold, conditions for determining the bifurcation direction and the stability of bifurcating periodic solution are derived. Some numerical simulations are carried out for illustrating the theoretical results.

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Acknowledgments

The authors wish to express their gratitude to the editors and the reviewers for the helpful comments. This research is supported by the Fundamental Research Funds for the Central Universities, National Nature Science Foundation of China (No.11601070) and Heilongjiang Provincial Natural Science Foundation (No.A2015016).

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  1. Department of Mathematics, Northeast Forestry University, Harbin, 150040, Heilongjiang, China

    Ruizhi Yang & Chunrui Zhang

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  1. Ruizhi Yang
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  2. Chunrui Zhang
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Correspondence to Chunrui Zhang.

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Yang, R., Zhang, C. Dynamics in a diffusive modified Leslie–Gower predator–prey model with time delay and prey harvesting. Nonlinear Dyn 87, 863–878 (2017). https://doi.org/10.1007/s11071-016-3084-7

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  • DOI: https://doi.org/10.1007/s11071-016-3084-7

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