The dynamics of a stoichiometric plant-herbivore model and its discrete analog
Stoichiometry-based models brought into sharp focus the importance of the nutritional quality of plant for herbivore-plant dynamics. Plant quality can dramatically affect the growth rate of the herbivores and may even lead to its extinction. These results stem from models continuous in time, which r...
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| 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.2007.4.29 |
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| author | Guangyu Sui Meng Fan Irakli Loladze Yang Kuang |
| author_facet | Guangyu Sui Meng Fan Irakli Loladze Yang Kuang |
| author_sort | Guangyu Sui |
| collection | DOAJ |
| description | Stoichiometry-based models brought into sharp focus the importance of the nutritional quality of plant for herbivore-plant dynamics. Plant quality can dramatically affect the growth rate of the herbivores and may even lead to its extinction. These results stem from models continuous in time, which raises the question of how robust they are to time discretization. Discrete time can be more appropriate for herbivores with non-overlapping generations, annual plants, and experimental data collected periodically. We analyze a continuous stoichiometric plant-herbivore model that is mechanistically formulated in [11]. We then introduce its discrete analog and compare the dynamics of the continuous and discrete models. This discrete model includes the discrete LKE model (Loladze, Kuang and Elser (2000)) as a limiting case. |
| format | Article |
| id | doaj-art-3ec9864d3a4b4c78aae8639624549e1e |
| 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-3ec9864d3a4b4c78aae8639624549e1e2025-01-24T01:52:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-10-0141294610.3934/mbe.2007.4.29The dynamics of a stoichiometric plant-herbivore model and its discrete analogGuangyu Sui0Meng Fan1Irakli Loladze2Yang Kuang3School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R.School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R.School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R.School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R.Stoichiometry-based models brought into sharp focus the importance of the nutritional quality of plant for herbivore-plant dynamics. Plant quality can dramatically affect the growth rate of the herbivores and may even lead to its extinction. These results stem from models continuous in time, which raises the question of how robust they are to time discretization. Discrete time can be more appropriate for herbivores with non-overlapping generations, annual plants, and experimental data collected periodically. We analyze a continuous stoichiometric plant-herbivore model that is mechanistically formulated in [11]. We then introduce its discrete analog and compare the dynamics of the continuous and discrete models. This discrete model includes the discrete LKE model (Loladze, Kuang and Elser (2000)) as a limiting case.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.29droop equationstoichiometrybifurcation.plant-herbivore interactiondiscrete model |
| spellingShingle | Guangyu Sui Meng Fan Irakli Loladze Yang Kuang The dynamics of a stoichiometric plant-herbivore model and its discrete analog Mathematical Biosciences and Engineering droop equation stoichiometry bifurcation. plant-herbivore interaction discrete model |
| title | The dynamics of a stoichiometric plant-herbivore model and its discrete analog |
| title_full | The dynamics of a stoichiometric plant-herbivore model and its discrete analog |
| title_fullStr | The dynamics of a stoichiometric plant-herbivore model and its discrete analog |
| title_full_unstemmed | The dynamics of a stoichiometric plant-herbivore model and its discrete analog |
| title_short | The dynamics of a stoichiometric plant-herbivore model and its discrete analog |
| title_sort | dynamics of a stoichiometric plant herbivore model and its discrete analog |
| topic | droop equation stoichiometry bifurcation. plant-herbivore interaction discrete model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.29 |
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