Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 24 October 2019 / Approved: 29 October 2019 / Online: 29 October 2019 (14:33:31 CET)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Mathematics 2019, 7, 1100
DOI: 10.3390/math7111100

Abstract

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 as well as the 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 occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

Subject Areas

fractional order differential equation; linear harvesting; stability analysis; lyapunov function; hopf bifurcation

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