The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting
Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The an...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2023-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/37/e3sconf_icosmed2023_03003.pdf |
| _version_ | 1797775942585679872 |
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| author | Panigoro Hasan S. Resmawan Resmawan Rahmi Emli Beta Muhammad Afrizal Sidik Amelia Tri Rahma |
| author_facet | Panigoro Hasan S. Resmawan Resmawan Rahmi Emli Beta Muhammad Afrizal Sidik Amelia Tri Rahma |
| author_sort | Panigoro Hasan S. |
| collection | DOAJ |
| description | Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically. |
| first_indexed | 2024-03-12T22:42:56Z |
| format | Article |
| id | doaj.art-1574a9d1cadb42d38bb5f290deb5d499 |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-03-12T22:42:56Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-1574a9d1cadb42d38bb5f290deb5d4992023-07-21T09:33:17ZengEDP SciencesE3S Web of Conferences2267-12422023-01-014000300310.1051/e3sconf/202340003003e3sconf_icosmed2023_03003The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear HarvestingPanigoro Hasan S.0Resmawan Resmawan1Rahmi Emli2Beta Muhammad Afrizal3Sidik Amelia Tri Rahma4Biomathematics Research Group, Universitas NegeriBiomathematics Research Group, Universitas NegeriBiomathematics Research Group, Universitas NegeriDepartment of Mathematics, Universitas NegeriDepartment of Mathematics, Universitas NegeriModeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically.https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/37/e3sconf_icosmed2023_03003.pdf |
| spellingShingle | Panigoro Hasan S. Resmawan Resmawan Rahmi Emli Beta Muhammad Afrizal Sidik Amelia Tri Rahma The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting E3S Web of Conferences |
| title | The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting |
| title_full | The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting |
| title_fullStr | The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting |
| title_full_unstemmed | The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting |
| title_short | The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting |
| title_sort | existence of a limit cycle of a discrete time lotka volterra model with fear effect and linear harvesting |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/37/e3sconf_icosmed2023_03003.pdf |
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