Travelling waves in a reaction-diffusion system modelling fungal mycelia

F. A. Davidson, B. D. Sleeman, J. W. Crawford

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We discuss travelling-wave solutions of a system of coupled reaction-diffusion equations used by the authors to describe the macroscopic behaviour of fungal mycelia. Such systems have been used in a multitude of applications; and, in particular, Merkin and Needham (1990, Proc. R. Soc. Lond. A 430, 315-45) have studied a certain formulation as a model for generic isothermal chemical reactions. We show that an alternative analysis provides more complete results in ascertaining the conditions under which travelling-wave solutions exist and that it allows a wider range of parameter values to be considered; this is essential to the application considered in the present case. Numerical investigations of travelling-wave solutions and the related initial-value problem are included to motivate and extend the analysis.

    Original languageEnglish
    Pages (from-to)237-257
    Number of pages21
    JournalIMA Journal of Applied Mathematics
    Volume58
    Issue number3
    DOIs
    Publication statusPublished - Jun 1997

    Fingerprint Dive into the research topics of 'Travelling waves in a reaction-diffusion system modelling fungal mycelia'. Together they form a unique fingerprint.

  • Cite this