Asymptotic stability of tri-trophic food chains sharing a common resource
Language English Country United States Media print-electronic
Document type Journal Article, Research Support, Non-U.S. Gov't, Research Support, U.S. Gov't, Non-P.H.S.
PubMed
26498384
DOI
10.1016/j.mbs.2015.10.005
PII: S0025-5564(15)00211-4
Knihovny.cz E-resources
- Keywords
- Competition, Food webs, Lyapunov function, Resilience, Stability,
- MeSH
- Biodiversity MeSH
- Models, Biological * MeSH
- Ecosystem MeSH
- Mathematical Concepts MeSH
- Food Chain * MeSH
- Animals MeSH
- Check Tag
- Animals MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't 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.
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