Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

• Ceyu Lei ^[1] ; Xiaoling Han ^[1] ; Weiming Wang ^[2]
  1. [1] Northwest Normal University

     Northwest Normal University

     China

     
  2. [2] Huaiyin Normal University

     Huaiyin Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we investigate the dynamics of a class of discrete predator–prey model with alternative prey. We prove the boundedness of the solution, the existence and local/global stability of equilibrium points of the model, and verify the existence of flip bifurcation and Neimark-Sacker bifurcation. In addition, we use the maximum Lyapunov exponent and isoperimetric diagrams to verify the existence of periodic structures namely Arnold tongue and the shrimp-shaped structures in bi-parameter spaces of a class of predator–prey model.