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Dynamical Analysis of a Discrete Amensalism System with the Beddington–DeAngelis Functional Response and Allee Effect for the Unaffected Species

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Abstract

This research involves a discrete amensalism system with the Beddington–DeAngelis functional response and Allee effect for the unaffected species. We begin by investigating the presence and local stability of fixed points. Then, utilizing the central manifold theorem and bifurcation theory, we analyze a variety of codimension one and codimension two bifurcations, which include transcritical, pitchfork, fold, flip, fold-flip and 1 : 2 strong resonance bifurcations. These theoretical findings suggest that Allee effect serves a crucial role in stabilizing the population sizes of both species. In addition, Allee effect would make the system spend more time to achieve its stable steady-state solution. They are illustrated via numerical simulations.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian, 350108, People’s Republic of China

    Qimei Zhou & Fengde Chen

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  1. Qimei Zhou
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  2. Fengde Chen
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QZ wrote the main manuscript text and Fengde Chen reviewed and edited the manuscript.

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Correspondence to Fengde Chen.

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Zhou, Q., Chen, F. Dynamical Analysis of a Discrete Amensalism System with the Beddington–DeAngelis Functional Response and Allee Effect for the Unaffected Species. Qual. Theory Dyn. Syst. 22, 16 (2023). https://doi.org/10.1007/s12346-022-00716-5

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