Using Numerical Bifurcation Analysis to Study Pattern Formation in Mussel Beds

Soft-bottomed mussel beds provide an important example of ecosystem-scale self-organisation. Field data from some intertidal regions shows banded patterns of mussels, running parallel to the shore. This paper demonstrates the use of numerical bifurcation methods to investigate in detail the predicti...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2016-01, Vol.11 (5), p.86-102
Main Author: Sherratt, J.A.
Format: Article
Language:English
Subjects:
35M10
92B05
92D40
Bifurcations
Ecosystems
Intertidal zone
Mathematical models
Mollusks
Mussels
numerical continuation
Numerical methods
Parameters
Pattern analysis
Pattern formation
periodic travelling wave
reaction-diffusion-advection
wavetrain
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Summary:Soft-bottomed mussel beds provide an important example of ecosystem-scale self-organisation. Field data from some intertidal regions shows banded patterns of mussels, running parallel to the shore. This paper demonstrates the use of numerical bifurcation methods to investigate in detail the predictions made by mathematical models concerning these patterns. The paper focusses on the “sediment accumulation model” proposed by Liu et al (Proc. R. Soc. Lond. B 14 (2012), 20120157). The author calculates the parameter region in which patterns exist, and the sub-region in which these patterns are stable as solutions of the original model. He then shows how his results can be used to explain numerical observations of history-dependent wavelength selection as parameters are varied slowly.
ISSN:1760-6101
0973-5348
1760-6101
DOI:10.1051/mmnp/201611506