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Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge

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Abstract

In this paper, a predator–prey model with Holling-II type functional response and a prey refuge is considered. The existence of Hopf bifurcations at the positive fixed point is established by analyzing its distribution of characteristic values. The stability and the directions of Hopf bifurcations of the model are derived for the variation of some crucial parameters. It is shown that these key parameters have a tremendous influence on the coexistence, the oscillation, and the stability of the considered model. Finally, numerical simulations are carried out to illustrate the validity of the results.

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Funding

This study was funded by the National Natural Science Foundation of China (11547006, 61503046, 11875135).

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Authors and Affiliations

  1. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, People’s Republic of China

    Yong Zhou, Wen Sun & Yinfang Song

  2. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, People’s Republic of China

    Zhigang Zheng

  3. Academy of Mathematics and Systems Science, CAS, Beijing, 100190, People’s Republic of China

    Jinhu Lu

  4. College of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Shihua Chen

Authors
  1. Yong Zhou
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  2. Wen Sun
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  3. Yinfang Song
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  4. Zhigang Zheng
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  5. Jinhu Lu
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  6. Shihua Chen
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Correspondence to Wen Sun.

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Zhou, Y., Sun, W., Song, Y. et al. Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge. Nonlinear Dyn 97, 1439–1450 (2019). https://doi.org/10.1007/s11071-019-05063-w

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  • DOI: https://doi.org/10.1007/s11071-019-05063-w

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