Population models with quasi-constant-yield harvest rates
One-dimensional logistic population models with quasi-constant-yield harvest rates are studied under the assumptions that a population inhabits a patch of dimensionless width and no members of the population can survive outside of the patch. The essential problem is to determine the size of the patc...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017029 |
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| author | Kunquan Lan Wei Lin |
| author_facet | Kunquan Lan Wei Lin |
| author_sort | Kunquan Lan |
| collection | DOAJ |
| description | One-dimensional logistic population models with quasi-constant-yield harvest rates are studied under the assumptions that a population inhabits a patch of dimensionless width and no members of the population can survive outside of the patch. The essential problem is to determine the size of the patch and the ranges of the harvesting rate functions under which the population survives or becomes extinct. This is the first paper which discusses such models with the Dirichlet boundary conditions and can tell the exact quantity of harvest rates of the species without having the population die out. The methodology is to establish new results on the existence of positive solutions of semi-positone Hammerstein integral equations using the fixed point index theory for compact maps defined on cones, and apply the new results to tackle the essential problem. It is expected that the established analytical results have broad applications in management of sustainable ecological systems. |
| format | Article |
| id | doaj-art-eb72be98a2e344189d0f96c35dafd70d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-eb72be98a2e344189d0f96c35dafd70d2025-01-24T02:39:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-03-0114246749010.3934/mbe.2017029Population models with quasi-constant-yield harvest ratesKunquan Lan0Wei Lin1Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, CanadaSchool of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, ChinaOne-dimensional logistic population models with quasi-constant-yield harvest rates are studied under the assumptions that a population inhabits a patch of dimensionless width and no members of the population can survive outside of the patch. The essential problem is to determine the size of the patch and the ranges of the harvesting rate functions under which the population survives or becomes extinct. This is the first paper which discusses such models with the Dirichlet boundary conditions and can tell the exact quantity of harvest rates of the species without having the population die out. The methodology is to establish new results on the existence of positive solutions of semi-positone Hammerstein integral equations using the fixed point index theory for compact maps defined on cones, and apply the new results to tackle the essential problem. It is expected that the established analytical results have broad applications in management of sustainable ecological systems.https://www.aimspress.com/article/doi/10.3934/mbe.2017029logistic population modelquasi-constant-yield harvest ratedirichlet boundary conditionsemi-positone integral equationfixed point index |
| spellingShingle | Kunquan Lan Wei Lin Population models with quasi-constant-yield harvest rates Mathematical Biosciences and Engineering logistic population model quasi-constant-yield harvest rate dirichlet boundary condition semi-positone integral equation fixed point index |
| title | Population models with quasi-constant-yield harvest rates |
| title_full | Population models with quasi-constant-yield harvest rates |
| title_fullStr | Population models with quasi-constant-yield harvest rates |
| title_full_unstemmed | Population models with quasi-constant-yield harvest rates |
| title_short | Population models with quasi-constant-yield harvest rates |
| title_sort | population models with quasi constant yield harvest rates |
| topic | logistic population model quasi-constant-yield harvest rate dirichlet boundary condition semi-positone integral equation fixed point index |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017029 |
| work_keys_str_mv | AT kunquanlan populationmodelswithquasiconstantyieldharvestrates AT weilin populationmodelswithquasiconstantyieldharvestrates |