Bifurcations, Permanence and Local Behavior of the Plant-Herbivore Model with Logistic Growth of Plant Biomass

• Kalabušic, S. ^[1] ; Pilav, E. ^[1]
  1. [1] University of Sarajevo

     University of Sarajevo

     Bosnia y Herzegovina

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper investigates the plant-herbivore model’s dynamics. The plant’s biomass without herbivores growth with logistic equation assuming that the herbivore (parasitization) occurs after the host’s density-dependent growth regulation occurs. We give a topological classification of the equilibrium points. We show that the boundary equilibrium undergoes the transcritical, fold, and period-doubling bifurcation, whereas the interior equilibrium undergoes a Neimark-Sacker bifurcation. We use the OGY method to control chaos produced by period-doubling bifurcation. The system exhibits bistability between the stable interior attractors in the interior and the stable attractors in the x−boundary logistic dynamics (periodic orbits and strange attractors) for particular numerical values of parameters. Sufficient conditions for the permanence of the plant-herbivores system are obtained, ensuring the coexistence of both species.