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Bifurcations, Permanence and Local Behavior of the Plant-Herbivore Model with Logistic Growth of Plant Biomass
Ist Teil von
Qualitative theory of dynamical systems, 2022-06, Vol.21 (2), Article 26
Ort / Verlag
Cham: Springer International Publishing
Erscheinungsjahr
2022
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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
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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.