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Local Collapses in the Truscott-Brindley Model

Published online by Cambridge University Press:  04 December 2008

I. Siekmann  and
H. Malchow
I. Siekmann*
Affiliation:
Institut für Umweltsystemforschung, Universität Osnabrück, 49076 Osnabrück, Germany
H. Malchow
Affiliation:
Institut für Umweltsystemforschung, Universität Osnabrück, 49076 Osnabrück, Germany
*
ivo.siekmann@uos.de
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Abstract

Relaxation oscillations are limit cycles with two clearly differenttime scales. In this article the spatio-temporal dynamics of astandard prey-predator system in the parameter region of relaxationoscillation is investigated. Both prey and predator population aredistributed irregularly at a relatively high average level between amaximal and a minimal value. However, the slowly developing complexpattern exhibits a feature of “inverse excitability”: Bothpopulations show collapses which occur erratically both in space andin time. The nature of these collapses is analysed statistically andit is shown that the model behaviour can be interpreted as aresolution of the paradox of enrichment.

Keywords

excitabilityslow-fast cyclesspatiotemporal patternsrelaxation oscillationsparadox ofenrichment
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 4: Patterns and waves in ecology and evolution (2) , 2008 , pp. 114 - 130
Copyright
© EDP Sciences, 2008

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