Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays

Xu Rui, Chen Lansun, M. A. J. Chaplain

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
    Original languageEnglish
    Pages (from-to)208-218
    Number of pages11
    JournalActa Mathematica Scientia (Series B)
    Volume23
    Issue number2
    Publication statusPublished - 2003

    Fingerprint

    Competitive System
    negative feedback
    Negative Feedback
    Lotka-Volterra System
    Global Asymptotic Stability
    Positive Solution
    Lotka-Volterra
    Interaction Effects
    Lyapunov Functional
    Type Systems
    Instantaneous
    Corollary
    Sufficient Conditions
    interactions

    Keywords

    • Finite delay
    • Infinite delay
    • Global asymptotic stability
    • Lyapunov functional

    Cite this

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    title = "Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays",
    abstract = "A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.",
    keywords = "Finite delay, Infinite delay, Global asymptotic stability, Lyapunov functional",
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    Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays. / Rui, Xu; Lansun, Chen; Chaplain, M. A. J.

    In: Acta Mathematica Scientia (Series B), Vol. 23, No. 2, 2003, p. 208-218.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays

    AU - Rui, Xu

    AU - Lansun, Chen

    AU - Chaplain, M. A. J.

    N1 - dc.publisher: Elsevier

    PY - 2003

    Y1 - 2003

    N2 - A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.

    AB - A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.

    KW - Finite delay

    KW - Infinite delay

    KW - Global asymptotic stability

    KW - Lyapunov functional

    M3 - Article

    VL - 23

    SP - 208

    EP - 218

    JO - Acta Mathematica Scientia (Series B)

    JF - Acta Mathematica Scientia (Series B)

    SN - 0252-9602

    IS - 2

    ER -