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A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting

A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear... <jats:p>We consider a model of predator–prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity and boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon’s theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurrence of Hopf bifurcation around the interior point is also shown analytically. At the end, we implemented the Predictor–Corrector scheme to perform some numerical simulations.</jats:p> http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics CrossRef

A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting

Mathematics , Volume 7 (11): 1100 – Nov 14, 2019

A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting


Abstract

<jats:p>We consider a model of predator–prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity and boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon’s theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurrence of Hopf bifurcation around the interior point is also shown analytically. At the end, we implemented the Predictor–Corrector scheme to perform some numerical simulations.</jats:p>

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Publisher
CrossRef
ISSN
2227-7390
DOI
10.3390/math7111100
Publisher site
See Article on Publisher Site

Abstract

<jats:p>We consider a model of predator–prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity and boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon’s theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurrence of Hopf bifurcation around the interior point is also shown analytically. At the end, we implemented the Predictor–Corrector scheme to perform some numerical simulations.</jats:p>

Journal

MathematicsCrossRef

Published: Nov 14, 2019

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