Optimal harvesting policy for the Beverton--Holt model
In this paper, we establish the exploitation of a single population modeled by the Beverton--Holt difference equation with periodic coefficients. We begin our investigation with the harvesting of a single autonomous population with logistic growth and show that the harvested logistic equation with p...
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016014 |
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| author | Martin Bohner Sabrina Streipert |
| author_facet | Martin Bohner Sabrina Streipert |
| author_sort | Martin Bohner |
| collection | DOAJ |
| description | In this paper, we establish the exploitation of a single population modeled by the Beverton--Holt difference equation with periodic coefficients. We begin our investigation with the harvesting of a single autonomous population with logistic growth and show that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, we approach the investigation of the optimal harvesting policy that maximizes the annual sustainable yield in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model. In the second part of the paper, we formulate the harvested Beverton--Holt model and derive the unique periodic solution, which globally attracts all its solutions. We continue our investigation by optimizing the sustainable yield with respect to the harvest effort. The results differ from the optimal harvesting policy for the continuous logistic model, which suggests a separate strategy for populations modeled by the Beverton--Holt difference equation. |
| format | Article |
| id | doaj-art-fcf9fb7014444d9a9d419b57a4955a90 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-fcf9fb7014444d9a9d419b57a4955a902025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113467369510.3934/mbe.2016014Optimal harvesting policy for the Beverton--Holt modelMartin Bohner0Sabrina Streipert1Missouri University of Science and Technology, 400 West, 12th Street, Rolla, MO 65409-0020Missouri University of Science and Technology, 400 West, 12th Street, Rolla, MO 65409-0020In this paper, we establish the exploitation of a single population modeled by the Beverton--Holt difference equation with periodic coefficients. We begin our investigation with the harvesting of a single autonomous population with logistic growth and show that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, we approach the investigation of the optimal harvesting policy that maximizes the annual sustainable yield in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model. In the second part of the paper, we formulate the harvested Beverton--Holt model and derive the unique periodic solution, which globally attracts all its solutions. We continue our investigation by optimizing the sustainable yield with respect to the harvest effort. The results differ from the optimal harvesting policy for the continuous logistic model, which suggests a separate strategy for populations modeled by the Beverton--Holt difference equation.https://www.aimspress.com/article/doi/10.3934/mbe.2016014maximum sustainable yield.difference equationslogistic growthperiodic solutionweighted jensen inequalityglobal stability |
| spellingShingle | Martin Bohner Sabrina Streipert Optimal harvesting policy for the Beverton--Holt model Mathematical Biosciences and Engineering maximum sustainable yield. difference equations logistic growth periodic solution weighted jensen inequality global stability |
| title | Optimal harvesting policy for the Beverton--Holt model |
| title_full | Optimal harvesting policy for the Beverton--Holt model |
| title_fullStr | Optimal harvesting policy for the Beverton--Holt model |
| title_full_unstemmed | Optimal harvesting policy for the Beverton--Holt model |
| title_short | Optimal harvesting policy for the Beverton--Holt model |
| title_sort | optimal harvesting policy for the beverton holt model |
| topic | maximum sustainable yield. difference equations logistic growth periodic solution weighted jensen inequality global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016014 |
| work_keys_str_mv | AT martinbohner optimalharvestingpolicyforthebevertonholtmodel AT sabrinastreipert optimalharvestingpolicyforthebevertonholtmodel |