Codimension-Two Bifurcation in a Class of a Discrete-Time Predator–Prey Interaction with Cannibalism

• Muhammad Asif Khan ^[1] ; Qamar Din ^[1]
  1. [1] University of Poonch Rawalakot
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
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• Resumen

  • The interplay of non-overlapping generations and cannibalism within prey populations can generate complex predator–prey relationships, significantly influencing population dynamics. This research investigates the complexities of codimension-two bifurcations in a discrete-time predator–prey model, distinguished by its inclusion of cannibalistic dynamics. Our study specifically investigates resonances with ratios of 1:2, 1:3, and 1:4, examining their influence on the dynamics of the predator–prey system in detail.

    The dynamic interplay between potent resonances and cannibalism reveals a fresh synergy, wherein resonances induce synchronized orbital behaviors, while cannibalism introduces further complexities into the predator–prey interaction. Gaining an understanding of these dynamics within the context of codimension-two bifurcation offers valuable insights into the intricate behaviors exhibited by the predator–prey model.

    These findings enhance our understanding of the intricate dynamics that emerge in discrete-time ecological systems featuring cannibalistic interactions.