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The role of strong Allee effect and protection zone on a diffusive prey–predator model

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Abstract

The influence of strong Allee effect and protection zone on the dynamical behavior and patterns of the reaction-diffusive model is investigated. Firstly, the existence and stability of the positive constant steady-states are determined. Secondly, we analyze the existence and nonexistence of nonconstant positive steady-states by the implicit function theorem, energy method and Leray–Schauder degree theory. Following, the dynamical properties are also obtained and in particular it is shown that the overexploitation phenomenon may occur. Finally, we show that the overexploitation phenomenon can be avoided by setting up a suitable protection zone for the prey. Hence, the strong Allee effect and protection zone enrich the complexity of the system.

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Acknowledgements

The authors are very grateful to the anonymous reviewers for their valuable comments and suggestions which have contributed considerably to the improved presentation of this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University, Kaifeng, 475001, Henan, People’s Republic of China

    Jia-Fang Zhang & Weiping Lou

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yu-Xia Wang

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  1. Jia-Fang Zhang
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  2. Weiping Lou
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Correspondence to Jia-Fang Zhang.

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Supported by the NSF of China (U1604180)

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Zhang, JF., Lou, W. & Wang, YX. The role of strong Allee effect and protection zone on a diffusive prey–predator model. Z. Angew. Math. Phys. 73, 41 (2022). https://doi.org/10.1007/s00033-022-01675-2

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  • DOI: https://doi.org/10.1007/s00033-022-01675-2

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