Using Numerical Bifurcation Analysis to Study Pattern Formation in Mussel Beds

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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.

Original languageEnglish
Pages (from-to)86-102
Number of pages17
JournalMathematical Modelling of Natural Phenomena
Volume11
Issue number5
Early online date7 Dec 2016
DOIs
Publication statusPublished - 7 Dec 2016

Keywords

  • Mussels
  • Numerical continuation
  • Pattern formation
  • Periodic travelling wave
  • Reaction-diffusion-advection
  • Wavetrain

ASJC Scopus subject areas

  • Modelling and Simulation

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