Stability in a diffusive food chain model with Michaelis-Menten functional response

Zhigui Lin, Michael Pedersen

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    Abstract

    This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    JournalNonlinear Analysis: Theory, Methods & Applications
    Volume57
    Issue number3
    Pages (from-to)421-433
    ISSN0362-546X
    DOIs
    Publication statusPublished - 2004

    Keywords

    • Reaction-diffusion
    • Predator
    • Global stability

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