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Ratio-Dependent Predator-Prey Model with Qiwu's Growth for Prey

Nijamuddin Ali, Krishnendu Sarkar, Lakshmi Narayan Guin

Abstract



Modelling of predation process of an eco-system becomes closer to the existent situation when response of both the species is believed in the modelling process. Ratio-dependent functional response is one of them. In this article, a prey-predator model is thought with Qiwu’s growth for prey and ratio-dependent Holling type II functional response predation development. The crucial mathematical features of the proposed model are analyzed with the help of equilibria, stability analysis, and bifurcation theory. The parametric space under which the system enters into a Hopf-bifurcation has been investigated. Explicit formula for determining the stability of bifurcating periodic solutions is driven by using normal form and central manifold theory. Our analytical findings are performed by numerical experiments. Biological implications of the analytical findings are talked about in the conclusion section.

Keywords


Prey-predator model; Ratio-dependent response; Stability; Hopf-bifurcation.

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