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Asymptotic stability of tri-trophic food chains sharing a common resource
I. Vrkoč, V. Křivan,
Jazyk angličtina Země Spojené státy americké
Typ dokumentu časopisecké články, práce podpořená grantem, Research Support, U.S. Gov't, Non-P.H.S.
- MeSH
- biodiverzita MeSH
- biologické modely * MeSH
- ekosystém MeSH
- matematické pojmy MeSH
- potravní řetězec * MeSH
- zvířata MeSH
- Check Tag
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Research Support, U.S. Gov't, Non-P.H.S. MeSH
One of the key results of the food web theory states that the interior equilibrium of a tri-trophic food chain described by the Lotka-Volterra type dynamics is globally asymptotically stable whenever it exists. This article extends this result to food webs consisting of several food chains sharing a common resource. A Lyapunov function for such food webs is constructed and asymptotic stability of the interior equilibrium is proved. Numerical simulations show that as the number of food chains increases, the real part of the leading eigenvalue, while still negative, approaches zero. Thus the resilience of such food webs decreases with the number of food chains in the web.
Citace poskytuje Crossref.org
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- $a Vrkoč, Ivo $u Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic. Electronic address: vrkoc@math.cas.cz.
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- $a One of the key results of the food web theory states that the interior equilibrium of a tri-trophic food chain described by the Lotka-Volterra type dynamics is globally asymptotically stable whenever it exists. This article extends this result to food webs consisting of several food chains sharing a common resource. A Lyapunov function for such food webs is constructed and asymptotic stability of the interior equilibrium is proved. Numerical simulations show that as the number of food chains increases, the real part of the leading eigenvalue, while still negative, approaches zero. Thus the resilience of such food webs decreases with the number of food chains in the web.
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- $a Křivan, Vlastimil $u Institute of Entomology, Biology Center, Czech Academy of Sciences, Branišovská 31, 370 05 České Budějovice, Czech Republic; Department of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branišovská 1760, 370 05 České Budějovice, Czech Republic. Electronic address: vlastimil.krivan@gmail.com.
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