Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting
We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existenc...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/167671 |
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| author | Mustafa Hasanbulli Svitlana P. Rogovchenko Yuriy V. Rogovchenko |
| author_facet | Mustafa Hasanbulli Svitlana P. Rogovchenko Yuriy V. Rogovchenko |
| author_sort | Mustafa Hasanbulli |
| collection | DOAJ |
| description | We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was
studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter σ associated with the intensity of harvesting is explored. As σ grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically. |
| format | Article |
| id | doaj-art-d38e0dcd84b64bc2846b6ea4971fdffe |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d38e0dcd84b64bc2846b6ea4971fdffe2025-02-03T05:58:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/167671167671Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield HarvestingMustafa Hasanbulli0Svitlana P. Rogovchenko1Yuriy V. Rogovchenko2Center for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University Albany, Auckland 0745, New ZealandDepartment of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, TurkeyDepartment of Mathematical Sciences, University of Agder, Serviceboks 422, 4604 Kristiansand, NorwayWe discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter σ associated with the intensity of harvesting is explored. As σ grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically.http://dx.doi.org/10.1155/2013/167671 |
| spellingShingle | Mustafa Hasanbulli Svitlana P. Rogovchenko Yuriy V. Rogovchenko Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting Journal of Applied Mathematics |
| title | Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting |
| title_full | Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting |
| title_fullStr | Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting |
| title_full_unstemmed | Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting |
| title_short | Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting |
| title_sort | dynamics of a single species in a fluctuating environment under periodic yield harvesting |
| url | http://dx.doi.org/10.1155/2013/167671 |
| work_keys_str_mv | AT mustafahasanbulli dynamicsofasinglespeciesinafluctuatingenvironmentunderperiodicyieldharvesting AT svitlanaprogovchenko dynamicsofasinglespeciesinafluctuatingenvironmentunderperiodicyieldharvesting AT yuriyvrogovchenko dynamicsofasinglespeciesinafluctuatingenvironmentunderperiodicyieldharvesting |