Optimal control for a size-structured predator-prey model in a polluted environment
In this paper, we deal with an optimal harvesting problem for a periodic predator-prey hybrid system dependent on size-structure in a polluted environment. In other words, a size-dependent model in an environment with a small toxicant content has been established. The well-posedness of state system...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2021-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/45/e3sconf_eeaphs2021_01004.pdf |
| _version_ | 1819013280428982272 |
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| author | Zhang Tainian Luo Zhixue |
| author_facet | Zhang Tainian Luo Zhixue |
| author_sort | Zhang Tainian |
| collection | DOAJ |
| description | In this paper, we deal with an optimal harvesting problem for a periodic predator-prey hybrid system dependent on size-structure in a polluted environment. In other words, a size-dependent model in an environment with a small toxicant content has been established. The well-posedness of state system is proved by using the fixed point theorem. The necessary optimality conditions are derived by tangent-normal cone technique in nonlinear functional analysis. The existence of a unique optimal harvesting policy is verified via the Ekeland’s variational principle. The optimal harvesting problem has an optimal harvesting policy, which has a Bang-Bang structure and provides a threshold for the optimal harvesting problem. Using the optimization theories and methods in mathematics to control phenomena of life. The objective function represents the total economic profit from the harvested population. Some theoretical results obtained in this paper provide a scientific theoretical basis for the practical application of the model. |
| first_indexed | 2024-12-21T01:57:26Z |
| format | Article |
| id | doaj.art-c633cde6c4fa4273a97af4817c6aae77 |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-12-21T01:57:26Z |
| publishDate | 2021-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-c633cde6c4fa4273a97af4817c6aae772022-12-21T19:19:45ZengEDP SciencesE3S Web of Conferences2267-12422021-01-012690100410.1051/e3sconf/202126901004e3sconf_eeaphs2021_01004Optimal control for a size-structured predator-prey model in a polluted environmentZhang Tainian0Luo Zhixue1School of Environmental and Municipal Engineering, Lanzhou Jiaotong UniversityDepartment of Mathematics, Lanzhou Jiaotong UniversityIn this paper, we deal with an optimal harvesting problem for a periodic predator-prey hybrid system dependent on size-structure in a polluted environment. In other words, a size-dependent model in an environment with a small toxicant content has been established. The well-posedness of state system is proved by using the fixed point theorem. The necessary optimality conditions are derived by tangent-normal cone technique in nonlinear functional analysis. The existence of a unique optimal harvesting policy is verified via the Ekeland’s variational principle. The optimal harvesting problem has an optimal harvesting policy, which has a Bang-Bang structure and provides a threshold for the optimal harvesting problem. Using the optimization theories and methods in mathematics to control phenomena of life. The objective function represents the total economic profit from the harvested population. Some theoretical results obtained in this paper provide a scientific theoretical basis for the practical application of the model.https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/45/e3sconf_eeaphs2021_01004.pdf |
| spellingShingle | Zhang Tainian Luo Zhixue Optimal control for a size-structured predator-prey model in a polluted environment E3S Web of Conferences |
| title | Optimal control for a size-structured predator-prey model in a polluted environment |
| title_full | Optimal control for a size-structured predator-prey model in a polluted environment |
| title_fullStr | Optimal control for a size-structured predator-prey model in a polluted environment |
| title_full_unstemmed | Optimal control for a size-structured predator-prey model in a polluted environment |
| title_short | Optimal control for a size-structured predator-prey model in a polluted environment |
| title_sort | optimal control for a size structured predator prey model in a polluted environment |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/45/e3sconf_eeaphs2021_01004.pdf |
| work_keys_str_mv | AT zhangtainian optimalcontrolforasizestructuredpredatorpreymodelinapollutedenvironment AT luozhixue optimalcontrolforasizestructuredpredatorpreymodelinapollutedenvironment |