Dynamics of a Discrete-Time Predator–Prey System with Holling II Functional Response

• Arias, Carlos F. ^[1] ; Blé, Gamaliel ^[1] ; Falconi, Manuel ^[2]
  1. [1] UJAT
  2. [2] UNAM
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
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• Resumen

  • The dynamics behavior of a discrete-time predator–prey system, with Holling II functional response, is analyzed. The model shows a rich dynamical behavior in the feasible region. Some invariant sets are found and parameter conditions for the existence and stability of the fixed points are given. A parameter region where the system exhibits either a period-doubling or a Neimark–Sacker bifurcation is shown. In addition, conditions are provided on parameters that lead to chaotic dynamics. Finally, to illustrate our theoretical analysis some numerical simulations are shown.