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

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Abstract

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.

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  1. Department of Mathematics, University of Sarajevo, 71000, Sarajevo, Bosnia and Herzegovina

    S. Kalabušić & E. Pilav

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  1. S. Kalabušić
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  2. E. Pilav
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Correspondence to S. Kalabušić.

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Kalabušić, S., Pilav, E. Bifurcations, Permanence and Local Behavior of the Plant-Herbivore Model with Logistic Growth of Plant Biomass. Qual. Theory Dyn. Syst. 21, 26 (2022). https://doi.org/10.1007/s12346-022-00561-6

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