Stability and optimal control for some classes of tritrophic systems
The objective of this paper is to study an optimal resource management problem for some classes of tritrophic systems composed by autotrophic resources (plants), bottom level consumers (herbivores) and top level consumers (humans). The first class of systems we discuss are linear chains, in which bi...
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.257 |
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| author | Luca Galbusera Sara Pasquali Gianni Gilioli |
| author_facet | Luca Galbusera Sara Pasquali Gianni Gilioli |
| author_sort | Luca Galbusera |
| collection | DOAJ |
| description | The objective of this paper is to study an optimal resource management problem for some classes of tritrophic systems composed by autotrophic resources (plants), bottom level consumers (herbivores) and top level consumers (humans). The first class of systems we discuss are linear chains, in which biomass flows from plants to herbivores, and from herbivores to humans. In the second class of systems humans are omnivorous and hence compete with herbivores for plant resources. Finally, in the third class of systems humans are omnivorous, but the plant resources are partitioned so that humans and herbivores do not complete for the same ones. The three trophic chains are expressed as Lotka-Volterra models, which seems to be a suitable choice in contexts where there is a shortage of food for the consumers. Our model parameters are taken from the literature on agro-pastoral systems in Sub-Saharan Africa. |
| format | Article |
| id | doaj-art-e0bef5b07c08477fa2835c3c32b81ab4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e0bef5b07c08477fa2835c3c32b81ab42025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111225728310.3934/mbe.2014.11.257Stability and optimal control for some classes of tritrophic systemsLuca Galbusera0Sara Pasquali1Gianni Gilioli2previously at CNR, Institute of Applied Mathematics and Information Technology “Enrico Magenes”, Via E. Bassini 15, 20133 MilanoCNR, Institute of Applied Mathematics and Information Technology “Enrico Magenes”, Via E. Bassini 15, 20133 MilanoDepartment of Molecular and Translational Medicine, University of Brescia, Viale Europa 11, 25125 BresciaThe objective of this paper is to study an optimal resource management problem for some classes of tritrophic systems composed by autotrophic resources (plants), bottom level consumers (herbivores) and top level consumers (humans). The first class of systems we discuss are linear chains, in which biomass flows from plants to herbivores, and from herbivores to humans. In the second class of systems humans are omnivorous and hence compete with herbivores for plant resources. Finally, in the third class of systems humans are omnivorous, but the plant resources are partitioned so that humans and herbivores do not complete for the same ones. The three trophic chains are expressed as Lotka-Volterra models, which seems to be a suitable choice in contexts where there is a shortage of food for the consumers. Our model parameters are taken from the literature on agro-pastoral systems in Sub-Saharan Africa.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.257lotka-volterratrophic systemstabilityoptimal control.coexistenceextinction |
| spellingShingle | Luca Galbusera Sara Pasquali Gianni Gilioli Stability and optimal control for some classes of tritrophic systems Mathematical Biosciences and Engineering lotka-volterra trophic system stability optimal control. coexistence extinction |
| title | Stability and optimal control for some classes of tritrophic systems |
| title_full | Stability and optimal control for some classes of tritrophic systems |
| title_fullStr | Stability and optimal control for some classes of tritrophic systems |
| title_full_unstemmed | Stability and optimal control for some classes of tritrophic systems |
| title_short | Stability and optimal control for some classes of tritrophic systems |
| title_sort | stability and optimal control for some classes of tritrophic systems |
| topic | lotka-volterra trophic system stability optimal control. coexistence extinction |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.257 |
| work_keys_str_mv | AT lucagalbusera stabilityandoptimalcontrolforsomeclassesoftritrophicsystems AT sarapasquali stabilityandoptimalcontrolforsomeclassesoftritrophicsystems AT giannigilioli stabilityandoptimalcontrolforsomeclassesoftritrophicsystems |