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On the stability-complexity relation for unsaturated semelpareous discrete food-chains
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.ORCID iD: 0000-0002-7261-0399
Högskolan i Finnmark.
2011 (English)In: Studies in mathematical sciences, ISSN 1923-8444, E-ISSN 1923-8452, Vol. 2, no 1, 157-182 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we formally prove that invading carnivores in thediscrete food-chain derived and preliminary analyzed inLindström (2002) always makes thesystem less stable and thus, limit the food-chain length in thecorresponding system. Hence, invading unsaturated carnivores arenot able to stabilize oscillatory dynamics.

What we prove constitutes a significant difference betweendiscrete and continuous food-chains. Actually, Freedman andWaltman (1977) related the stabilizingproperties of an invading carnivore in continuous food-chains to absence of saturation: An unsaturated carnivore keeps at least oneinterior equilibrium - if one exists - locally stable.

One consequence is that the dynamics of unsaturated discretefood-chains display similarities with saturated continuousfood-chains. Indeed, discrete dynamics seem to have a similardestabilizing impact on the dynamics as saturation has.

Place, publisher, year, edition, pages
2011. Vol. 2, no 1, 157-182 p.
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-10620OAI: oai:DiVA.org:lnu-10620DiVA: diva2:395529
Available from: 2011-02-07 Created: 2011-02-07 Last updated: 2017-01-24Bibliographically approved

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CiteExportLink to record
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  • apa
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