Suryanto, A.; Darti, I.; S. Panigoro, H.; Kilicman, A. A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting. Mathematics2019, 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.
Suryanto, A.; Darti, I.; S. Panigoro, H.; Kilicman, A. A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting. Mathematics2019, 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.
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.
Keywords
fractional order differential equation; linear harvesting; stability analysis; lyapunov function; hopf bifurcation
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
