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Stability and global Hopf bifurcation in a Leslie–Gower predator-prey model with stage structure for prey

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Abstract

This paper is concerned with a predator-prey model with Leslie–Gower functional response and stage structure for prey. By regarding time delay as the bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of Hopf bifurcation are given. Some explicit formulas determining the properties of Hopf bifurcation are established by using the normal form method and center manifold theorem. The global continuation of periodic solutions bifurcating from the positive equilibrium is given due to a global Hopf bifurcation result for functional differential equations. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

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Acknowledgements

The authors convey their sincere thanks and gratitude to four reviewers for their suggestions towards the improvement of the manuscript. This work is supported by the National Natural Science Foundation of China (Grant Nos. 1661050 and 11461041), and the Development Program for HongLiu Outstanding Young Teachers in Lanzhou University of Technology (Q201308).

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Authors and Affiliations

  1. School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, China

    Xin-You Meng, Hai-Feng Huo & Xiao-Bing Zhang

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  1. Xin-You Meng
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  2. Hai-Feng Huo
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  3. Xiao-Bing Zhang
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Correspondence to Xin-You Meng.

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Meng, XY., Huo, HF. & Zhang, XB. Stability and global Hopf bifurcation in a Leslie–Gower predator-prey model with stage structure for prey. J. Appl. Math. Comput. 60, 1–25 (2019). https://doi.org/10.1007/s12190-018-1201-0

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  • DOI: https://doi.org/10.1007/s12190-018-1201-0

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