Oscillation in Pest Population and Its Management: A Mathematical Study
We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/653080 |
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| author | Samit Bhattacharyya Suma Ghosh |
| author_facet | Samit Bhattacharyya Suma Ghosh |
| author_sort | Samit Bhattacharyya |
| collection | DOAJ |
| description | We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case. |
| format | Article |
| id | doaj-art-261a930ee43b4966bf1487ca1063c35c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-261a930ee43b4966bf1487ca1063c35c2025-08-20T02:04:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/653080653080Oscillation in Pest Population and Its Management: A Mathematical StudySamit Bhattacharyya0Suma Ghosh1Departments of Mathematics and Biology, University of Utah, Salt Lake City, UT 84112, USADepartments of Mathematics and Biology, University of Utah, Salt Lake City, UT 84112, USAWe study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case.http://dx.doi.org/10.1155/2013/653080 |
| spellingShingle | Samit Bhattacharyya Suma Ghosh Oscillation in Pest Population and Its Management: A Mathematical Study International Journal of Mathematics and Mathematical Sciences |
| title | Oscillation in Pest Population and Its Management: A Mathematical Study |
| title_full | Oscillation in Pest Population and Its Management: A Mathematical Study |
| title_fullStr | Oscillation in Pest Population and Its Management: A Mathematical Study |
| title_full_unstemmed | Oscillation in Pest Population and Its Management: A Mathematical Study |
| title_short | Oscillation in Pest Population and Its Management: A Mathematical Study |
| title_sort | oscillation in pest population and its management a mathematical study |
| url | http://dx.doi.org/10.1155/2013/653080 |
| work_keys_str_mv | AT samitbhattacharyya oscillationinpestpopulationanditsmanagementamathematicalstudy AT sumaghosh oscillationinpestpopulationanditsmanagementamathematicalstudy |