A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting

Citation

Suryanto, Agus and Darti, Isnani and Panigoro, Hasan S. and Kilicman, Adem (2019) A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting. Mathematics, 7 (11). art. no. 1100. pp. 1-13. ISSN 2227-7390

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 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.

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Official URL or Download Paper: https://www.mdpi.com/2227-7390/7/11/1100

Additional Metadata

Item Type:	Article
Divisions:	Faculty of Science
DOI Number:	https://doi.org/10.3390/math7111100
Publisher:	MDPI
Keywords:	Fractional-order differential equation; Linear harvesting; Stability analysis; Lyapunov function; Hopf bifurcation
Depositing User:	Nabilah Mustapa
Date Deposited:	04 May 2020 15:59
Last Modified:	04 May 2020 15:59
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/math7111100
URI:	http://psasir.upm.edu.my/id/eprint/38218
Statistic Details:	View Download Statistic

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