Pattern formation for a model of plankton allelopathy with cross-diffusion

C.R. Tian, Lai Zhang, Z.G. Lin

    Research output: Contribution to journalJournal articleResearchpeer-review


    In this paper, we develop a theoretical framework for investigating spatial patterns on plankton allelopathy with cross-diffusion. We show that under some conditions the cross-diffusion is able to induce the Turing instability, which is further confirmed by the numerical simulations. Moreover, applying the Leray–Schauder degree theory, we demonstrate that the cross-diffusion leads to an inhomogeneous stationary pattern provided with even stronger conditions. Finally, the wavenumber and the type of pattern selection are computed numerically. Our theoretical results of the spatial pattern are coincident with the experimental observations.
    Original languageEnglish
    JournalJournal of the Franklin Institute
    Issue number8
    Pages (from-to)1947–1964
    Publication statusPublished - 2011


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