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

• Qimei Zhou ^[1] ; Fengde Chen ^[1]
  1. [1] Fuzhou University

     Fuzhou University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • 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.