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Stability and bifurcation of a discrete predator-prey system with Allee effect and other food resource for the predators

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Abstract

Concerned in this paper is a discrete predator-prey system with Allee effect and other food resources for the predators. The conditions on the existence and stability of fixed points are obtained. It is shown that the system can undergo fold bifurcation and flip bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations are provided to illustrate the feasibility of the main results and the influence of Allee effect on the stability of the system. Our study indicates that other food resources for the predator can enrich the dynamical behaviours of the system, including cascades of period-doubling bifurcation in orbits of period-2, 4, 8, and chaotic sets.

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Acknowledgements

This work was supported partially by the Natural Science Foundation of Fujian Province (2020J01499).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, Fujian, People’s Republic of China

    Jialin Chen, Zhenliang Zhu & Fengde Chen

  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Ontario, Canada

    Yuming Chen

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  1. Jialin Chen
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Correspondence to Yuming Chen.

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Chen, J., Chen, Y., Zhu, Z. et al. Stability and bifurcation of a discrete predator-prey system with Allee effect and other food resource for the predators. J. Appl. Math. Comput. 69, 529–548 (2023). https://doi.org/10.1007/s12190-022-01764-5

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  • DOI: https://doi.org/10.1007/s12190-022-01764-5

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