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Article

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

1
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia
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Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Gorontalo 96128, Indonesia
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Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1100; https://doi.org/10.3390/math7111100
Received: 24 October 2019 / Revised: 7 November 2019 / Accepted: 8 November 2019 / Published: 14 November 2019
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. View Full-Text
Keywords: fractional-order differential equation; linear harvesting; stability analysis; Lyapunov function; Hopf bifurcation fractional-order differential equation; linear harvesting; stability analysis; Lyapunov function; Hopf bifurcation
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MDPI and ACS Style

Suryanto, A.; Darti, I.; S. Panigoro, H.; Kilicman, A. A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting. Mathematics 2019, 7, 1100. https://doi.org/10.3390/math7111100

AMA Style

Suryanto A, Darti I, S. Panigoro H, Kilicman A. A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting. Mathematics. 2019; 7(11):1100. https://doi.org/10.3390/math7111100

Chicago/Turabian Style

Suryanto, Agus, Isnani Darti, Hasan S. Panigoro, and Adem Kilicman. 2019. "A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting" Mathematics 7, no. 11: 1100. https://doi.org/10.3390/math7111100

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