Math. Model. Nat. Phenom.
Volume 3, Number 4, 2008Patterns and waves in ecology and evolution (2)
|Page(s)||114 - 130|
|Published online||04 December 2008|
Local Collapses in the Truscott-Brindley Model
Institut für Umweltsystemforschung,
Universität Osnabrück, 49076 Osnabrück, Germany
Corresponding author: email@example.com
Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses which occur erratically both in space and in time. The nature of these collapses is analysed statistically and it is shown that the model behaviour can be interpreted as a resolution of the paradox of enrichment.
Mathematics Subject Classification: 35K57 / 35Q80 / 60H15
Key words: excitability / slow-fast cycles / spatiotemporal patterns / relaxation oscillations / paradox of enrichment
© EDP Sciences, 2008
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