Forest defoliation scenarios
We consider the mathematical model originally created by Ludwig, Jones, and Holling to model the infestation of spruce forests in New Brunswick by the spruce budworm. With biologically plausible parameter values, the dimensionless version of the model contains small parameters derived from the time...
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| Format: | Article |
| Language: | English |
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AIMS Press
2006-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.15 |
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| author | Glenn Ledder |
| author_facet | Glenn Ledder |
| author_sort | Glenn Ledder |
| collection | DOAJ |
| description | We consider the mathematical model originally created by Ludwig, Jones, and Holling to model the infestation of spruce forests in New Brunswick by the spruce budworm. With biologically plausible parameter values, the dimensionless version of the model contains small parameters derived from the time scales of the state variables and smaller parameters derived from the relative importance of different population change mechanisms. The small time-scale parameters introduce a singular perturbation structure to solutions, with one variable changing on a slow time scale and two changing on a fast time scale. The smaller process-scale parameters allow for the existence of equilibria at vastly different orders of magnitude. These changes in scale of the state variables result in fast dynamics not associated with the time scales. For any given set of parameters, the observed dynamics is a mixture of time-scale effects with process-scale effects. We identify and analyze the different scenarios that can occur and indicate the relevant regions in the parameter space corresponding to each. |
| format | Article |
| id | doaj-art-e64f0c491f4d4d85907893b5df22b079 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e64f0c491f4d4d85907893b5df22b0792025-01-24T01:52:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-10-0141152810.3934/mbe.2007.4.15Forest defoliation scenariosGlenn Ledder0Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130We consider the mathematical model originally created by Ludwig, Jones, and Holling to model the infestation of spruce forests in New Brunswick by the spruce budworm. With biologically plausible parameter values, the dimensionless version of the model contains small parameters derived from the time scales of the state variables and smaller parameters derived from the relative importance of different population change mechanisms. The small time-scale parameters introduce a singular perturbation structure to solutions, with one variable changing on a slow time scale and two changing on a fast time scale. The smaller process-scale parameters allow for the existence of equilibria at vastly different orders of magnitude. These changes in scale of the state variables result in fast dynamics not associated with the time scales. For any given set of parameters, the observed dynamics is a mixture of time-scale effects with process-scale effects. We identify and analyze the different scenarios that can occur and indicate the relevant regions in the parameter space corresponding to each.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.15defoliationsingular perturbationspruce budworm. |
| spellingShingle | Glenn Ledder Forest defoliation scenarios Mathematical Biosciences and Engineering defoliation singular perturbation spruce budworm. |
| title | Forest defoliation scenarios |
| title_full | Forest defoliation scenarios |
| title_fullStr | Forest defoliation scenarios |
| title_full_unstemmed | Forest defoliation scenarios |
| title_short | Forest defoliation scenarios |
| title_sort | forest defoliation scenarios |
| topic | defoliation singular perturbation spruce budworm. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.15 |
| work_keys_str_mv | AT glennledder forestdefoliationscenarios |