A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting
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 ex...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38218/ http://psasir.upm.edu.my/id/eprint/38218/1/38218.pdf |
| _version_ | 1848848818677743616 |
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| author | Suryanto, Agus Darti, Isnani Panigoro, Hasan S. Kilicman, Adem |
| author_facet | Suryanto, Agus Darti, Isnani Panigoro, Hasan S. Kilicman, Adem |
| author_sort | Suryanto, Agus |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T09:40:33Z |
| format | Article |
| id | upm-38218 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:40:33Z |
| publishDate | 2019 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-382182020-05-04T15:59:41Z http://psasir.upm.edu.my/id/eprint/38218/ A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting Suryanto, Agus Darti, Isnani Panigoro, Hasan S. Kilicman, Adem 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. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/38218/1/38218.pdf 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 https://www.mdpi.com/2227-7390/7/11/1100 10.3390/math7111100 |
| spellingShingle | Suryanto, Agus Darti, Isnani Panigoro, Hasan S. Kilicman, Adem A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| title | A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| title_full | A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| title_fullStr | A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| title_full_unstemmed | A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| title_short | A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| title_sort | fractional-order predator–prey model with ratio-dependent functional response and linear harvesting |
| url | http://psasir.upm.edu.my/id/eprint/38218/ http://psasir.upm.edu.my/id/eprint/38218/ http://psasir.upm.edu.my/id/eprint/38218/ http://psasir.upm.edu.my/id/eprint/38218/1/38218.pdf |