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Impact of discontinuous harvesting on a diffusive predator–prey model with fear and Allee effect

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Abstract

In this paper, we investigate a diffusive predator–prey model with discontinuous harvesting. The model’s boundedness is explored, as well as the presence and stability of equilibria, Hopf bifurcation, and Turing bifurcation. Additionally, we establish the sliding mode’s existence and study different types of sliding mode bifurcation, including boundary node, grazing, buckling, and crossing bifurcation. Additionally, computer simulations demonstrate that the system may develop a variety of spatial patterns depending on the harvesting threshold, the cost of fear, and the initial conditions.

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Acknowledgements

The work is supported by National Science Foundation of China under Grant 11971013.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xuebing Zhang

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

    Hongyong Zhao

  3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C5S7, Canada

    Yuan Yuan

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  1. Xuebing Zhang
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  2. Hongyong Zhao
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  3. Yuan Yuan
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Correspondence to Hongyong Zhao.

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Zhang, X., Zhao, H. & Yuan, Y. Impact of discontinuous harvesting on a diffusive predator–prey model with fear and Allee effect. Z. Angew. Math. Phys. 73, 168 (2022). https://doi.org/10.1007/s00033-022-01807-8

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  • DOI: https://doi.org/10.1007/s00033-022-01807-8

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