Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge
In this study, we implement a Nonstandard Finite Difference (NSFD) scheme for a predator-prey model involving cannibalism and refuge in predator. The scheme which is considered as a discrete dynamical system is analyzed. The performed analysis includes the determination of equilibrium point and its...
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| Format: | Article |
| Language: | English |
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Indonesian Bio-Mathematical Society
2023-07-01
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| Series: | Communication in Biomathematical Sciences |
| Subjects: | |
| Online Access: | https://journals.itb.ac.id/index.php/cbms/article/view/20040 |
| _version_ | 1827308950634102784 |
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| author | Maya Rayungsari Agus Suryanto W. M. Kusumawinahyu Isnani Darti |
| author_facet | Maya Rayungsari Agus Suryanto W. M. Kusumawinahyu Isnani Darti |
| author_sort | Maya Rayungsari |
| collection | DOAJ |
| description | In this study, we implement a Nonstandard Finite Difference (NSFD) scheme for a predator-prey model involving cannibalism and refuge in predator. The scheme which is considered as a discrete dynamical system is analyzed. The performed analysis includes the determination of equilibrium point and its local stability. The system has four equilibrium points, namely the origin, the prey extinction point, the predator extinction point, and the coexistence point, which have exactly the same form and existence conditions as those in continuous system. The local stability of each first three equilibrium points is consistent with the one in continuous system. The stability of the coexistence point depends on the integration time step size. Nevertheless, the NSFD scheme allows us to choose the integration time step size for the solution to converge to a feasible point more flexible than the Euler and 4th order Runge-Kutta schemes. These are shown via numerical simulations. |
| first_indexed | 2024-04-24T19:19:39Z |
| format | Article |
| id | doaj.art-63bb4aae91e3472aa14018aee6a1d802 |
| institution | Directory Open Access Journal |
| issn | 2549-2896 |
| language | English |
| last_indexed | 2024-04-24T19:19:39Z |
| publishDate | 2023-07-01 |
| publisher | Indonesian Bio-Mathematical Society |
| record_format | Article |
| series | Communication in Biomathematical Sciences |
| spelling | doaj.art-63bb4aae91e3472aa14018aee6a1d8022024-03-26T01:29:13ZengIndonesian Bio-Mathematical SocietyCommunication in Biomathematical Sciences2549-28962023-07-0161112310.5614/cbms.2023.6.1.220632Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and RefugeMaya Rayungsari0Agus Suryanto1W. M. Kusumawinahyu2Isnani Darti3Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia & Department of Mathematics Education, Faculty of Pedagogy and Psychology, PGRI Wiranegara University, Pasuruan 67118, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, IndonesiaIn this study, we implement a Nonstandard Finite Difference (NSFD) scheme for a predator-prey model involving cannibalism and refuge in predator. The scheme which is considered as a discrete dynamical system is analyzed. The performed analysis includes the determination of equilibrium point and its local stability. The system has four equilibrium points, namely the origin, the prey extinction point, the predator extinction point, and the coexistence point, which have exactly the same form and existence conditions as those in continuous system. The local stability of each first three equilibrium points is consistent with the one in continuous system. The stability of the coexistence point depends on the integration time step size. Nevertheless, the NSFD scheme allows us to choose the integration time step size for the solution to converge to a feasible point more flexible than the Euler and 4th order Runge-Kutta schemes. These are shown via numerical simulations.https://journals.itb.ac.id/index.php/cbms/article/view/20040nonstandard finite difference schemepredator-prey modelcannibalismrefuge |
| spellingShingle | Maya Rayungsari Agus Suryanto W. M. Kusumawinahyu Isnani Darti Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge Communication in Biomathematical Sciences nonstandard finite difference scheme predator-prey model cannibalism refuge |
| title | Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge |
| title_full | Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge |
| title_fullStr | Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge |
| title_full_unstemmed | Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge |
| title_short | Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge |
| title_sort | nonstandard numerical scheme for a predator prey model involving predator cannibalism and refuge |
| topic | nonstandard finite difference scheme predator-prey model cannibalism refuge |
| url | https://journals.itb.ac.id/index.php/cbms/article/view/20040 |
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