Using Numerical Bifurcation Analysis to Study Pattern Formation in Mussel Beds

Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

^* Corresponding author. E-mail: j.a.sherratt@hw.ac.uk

Abstract

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.