Local Collapses in the Truscott-Brindley Model

I. Siekmann; H. Malchow

Mathematical Modelling of Natural Phenomena (2008)

  • Volume: 3, Issue: 4, page 114-130
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Siekmann, I., and Malchow, H.. "Local Collapses in the Truscott-Brindley Model." Mathematical Modelling of Natural Phenomena 3.4 (2008): 114-130. <http://eudml.org/doc/222271>.

@article{Siekmann2008,
abstract = { 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.},
author = {Siekmann, I., Malchow, H.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {excitability; slow-fast cycles; spatiotemporal patterns; relaxation oscillations; paradox of enrichment; spatiotemporal patterns; paradox of enrichment},
language = {eng},
month = {12},
number = {4},
pages = {114-130},
publisher = {EDP Sciences},
title = {Local Collapses in the Truscott-Brindley Model},
url = {http://eudml.org/doc/222271},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Siekmann, I.
AU - Malchow, H.
TI - Local Collapses in the Truscott-Brindley Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/12//
PB - EDP Sciences
VL - 3
IS - 4
SP - 114
EP - 130
AB - 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.
LA - eng
KW - excitability; slow-fast cycles; spatiotemporal patterns; relaxation oscillations; paradox of enrichment; spatiotemporal patterns; paradox of enrichment
UR - http://eudml.org/doc/222271
ER -

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