Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations

S. A. Gourley, N. F. Britton, M. A. J. Chaplain, H. M. Byrne

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    9 Citations (Scopus)

    Abstract

    Potential mechanisms for stabilising and destabilising the spatially uniform steady states of systems of reaction-diffusion equations are examined. In the first instance the effect of introducing small periodic perturbations of the diffusion coefficients in a general system of reaction-diffusion equations is studied. Analytical results are proved for the case where the uniform steady state is marginally stable and demonstrate that the effect on the original system of such perturbations is one of stabilisation. Numerical simulations carried out on an ecological model of Levin and Segel (1976) confirm the analysis as well as extending it to the case where the perturbations are no longer small. Spatio-temporal delay is then introduced into the model. Analytical and numerical results are presented which show that the effect of the delay is to destabilise the original system.
    Original languageEnglish
    Pages (from-to)857-877
    Number of pages21
    JournalJournal of Mathematical Biology
    Volume34
    Issue number8
    DOIs
    Publication statusPublished - Sep 1996

    Keywords

    • Reaction-diffusion equations
    • Time-periodic diffusion coefficients
    • Spatio-temporal delay

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