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Local Collapses in the Truscott-Brindley Model

I. SiekmannH. Malchow — 2008

Mathematical Modelling of Natural Phenomena

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...

From Bistability to Coupling-Induced Oscillations in a Two-Habitat Model for the Rotifer Population Dynamics

A. B. MedvinskyM. M. GonikA. V. RusakovH. Malchow — 2008

Mathematical Modelling of Natural Phenomena

We study the role of interactions between habitats in rotifer dynamics. For this purpose we use a modified version of the Consensus model. The Consensus model has been shown to be realistic enough to reproduce distinguishing features of the rotifer species dynamics. Being uncoupled, intrinsically bistable rotifer populations, which inhabit the regions under different environmental conditions, do not impact each other. We show that migration of the rotifers between the habitats leads to the transformation...

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