Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each spec...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2018-01-01
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| Series: | E3S Web of Conferences |
| Subjects: | |
| Online Access: | https://doi.org/10.1051/e3sconf/20187306001 |
| _version_ | 1818916136735997952 |
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| author | Dita Anies Munawwaroh Sutimin Siti Khabibah |
| author_facet | Dita Anies Munawwaroh Sutimin Siti Khabibah |
| author_sort | Dita Anies Munawwaroh |
| collection | DOAJ |
| description | We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin’s maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting. |
| first_indexed | 2024-12-20T00:13:23Z |
| format | Article |
| id | doaj.art-335b81dde1ed43a8a6c8d047adfbb643 |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-12-20T00:13:23Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-335b81dde1ed43a8a6c8d047adfbb6432022-12-21T20:00:26ZengEDP SciencesE3S Web of Conferences2267-12422018-01-01730600110.1051/e3sconf/20187306001e3sconf_icenis18_06001Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and ToxicityDita Anies Munawwaroh0Sutimin1Siti Khabibah2Departement of Mathematics, Faculty of Sciences and Mathematics, Universitas DiponegoroDepartement of Mathematics, Faculty of Sciences and Mathematics, Universitas DiponegoroDepartement of Mathematics, Faculty of Sciences and Mathematics, Universitas DiponegoroWe proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin’s maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.https://doi.org/10.1051/e3sconf/20187306001Prey-predatorharvestingequilibriumstability |
| spellingShingle | Dita Anies Munawwaroh Sutimin Siti Khabibah Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity E3S Web of Conferences Prey-predator harvesting equilibrium stability |
| title | Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity |
| title_full | Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity |
| title_fullStr | Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity |
| title_full_unstemmed | Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity |
| title_short | Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity |
| title_sort | analysis of a prey predator fishing model for harvesting with the limited effect of density and toxicity |
| topic | Prey-predator harvesting equilibrium stability |
| url | https://doi.org/10.1051/e3sconf/20187306001 |
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