Turing instabilities and pattern formation in a benthic nutrient-microorganism system

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2004, 1(1): 111-130. doi: 10.3934/mbe.2004.1.111

Turing instabilities and pattern formation in a benthic nutrient-microorganism system

Martin Baurmann ^1, , Wolfgang Ebenhöh ^1, and Ulrike Feudel ^1,

1.	Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität Oldenburg, PF 2503, 26111 Oldenburg, Germany, Germany, Germany

Received March 2004 Revised March 2004 Published March 2004

Abstract
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In general, the distributions of nutrients and microorganisms in sediments show complex spatio-temporal patterns, which often cannot be explained as resulting exclusively from the temporal fluctuations of environmental conditions and the inhomogeneity of the studied sediment's material. We studied the dynamics of one population of microorganisms feeding on a nutrient in a simple model, taking into account that the considered bacteria can be in an active or in a dormant state. Using this model, we show that the formation of spatio-temporal patterns can be the consequence of the interaction between predation and transport processes. Employing the model on a two-dimensional vertical domain, we show by simulations which patterns can arise. Depending on the strength of bioirrigation, we observe stripes or "hot spots'' (or "cold spots'') with high (or low) microbiological activity. A detailed study regarding the effect of non-homogeneous (depth dependent) forcing by bioirrigation shows that different patterns can appear in different depths.

Keywords: pattern formation, reaction-diffusion models, Turing instability, sediment..

Mathematics Subject Classification: 92D25, 92D4.

Citation: Martin Baurmann, Wolfgang Ebenhöh, Ulrike Feudel. Turing instabilities and pattern formation in a benthic nutrient-microorganism system. Mathematical Biosciences & Engineering, 2004, 1 (1) : 111-130. doi: 10.3934/mbe.2004.1.111

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