Periodic solution for a three-species Lotka-Volterra food-chain model with time delays

Rui Xu, M. A. J. Chaplain, F. A. Davidson

    Research output: Contribution to journalArticlepeer-review

    21 Citations (Scopus)

    Abstract

    A delayed three-species periodic Lotka-Volterra food-chain model without instantaneousnegative feedback is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness, and global stability of positive periodic solutions of the system. Computer simulations are presented to illustrate the conclusions.
    Original languageEnglish
    Pages (from-to)823-837
    Number of pages15
    JournalMathematical and Computer Modelling
    Volume40
    Issue number7-8
    DOIs
    Publication statusPublished - 2004

    Keywords

    • Food-chain model
    • Time delay
    • Periodic solution
    • Coincidence degree
    • Global stability

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