Dynamics of Fractional Order Predator Prey Models with Refuge and Allee Effect in Prey: With and Without Time Delay

• Qi Wang ^[1] ; Renji Han ^[2]
  1. [1] Anhui University

     Anhui University

     China

     
  2. [2] Zhejiang University of Science and Technology

     Zhejiang University of Science and Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we consider the dynamics of Caputo fractional order predator–prey models with Allee effect in prey and refuge in proportion to the two species. We first investigate the model without delay including the well-posedness, the existence of nonnegative equilibrium, and the global stability for all non-negative equilibria, and the fractional order Hopf bifurcation of the coexistence equilibrium, which indicates that the combination effect of Allee effect and prey refuge on system dynamics. Then, for the delayed model, we show that the coexistence equilibrium is locally asymptotically stable for any delay under certain conditions. Finally, numerical simulation is given to display the validity of the main results, and it also reveals the differences in dynamics between integer order and fractional order systems.

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