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Harvesting, Hopf Bifurcation and Chaos in Three Species Food Chain Model with Beddington–DeAngelis Type Functional Response

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Abstract:

The dynamical relationship between predator and prey can be represented by the prey functional response which refers to the change in the density of prey attached per unit time per predator as the prey density changes. In this paper, three-species food chain model with Beddington–DeAngelis type functional response is considered and found solution both analytically and numerically. We investigate the Hopf bifurcation and Chaos of the system at mortality rate ( ) of predator with the help of computer simulations. Butler-Mc Gehee lemma is used to identify the condition which influences the persistence of the system. We also study the effect of Harvesting on prey species. Harvesting has a strong impact on the dynamic evolution of a population. To a certain extent, it can control the long-term stationary density of population efficiently. However, it can also lead to the incorporation of a positive extinction probability and therefore to potential extinction in finite time. Our result suggests that the mortality rate of predator species have the ability to control the chaotic dynamics. Keywords: Food Chain Model, Stability, Persistence,Harvesting, Chaotic Attractor, Hopf Bifurcation

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