Modelling and analysis of a competitive model with stage structure

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

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.
    Original languageEnglish
    Pages (from-to)159-175
    Number of pages17
    JournalMathematical and Computer Modelling
    Volume41
    Issue number2-3
    DOIs
    Publication statusPublished - 2005

    Fingerprint

    Stage Structure
    Stage-structured
    Competition Model
    Modeling
    Mawhin's Continuation Theorem
    Coincidence Degree Theory
    Lotka-Volterra
    Model
    Bistability
    Sufficient Conditions
    Positive Periodic Solution
    Coefficient
    Periodic Functions
    Global Stability
    Dynamical Behavior
    Coexistence
    Lyapunov Function
    Continuous Function
    Non-negative
    Lyapunov functions

    Keywords

    • Stage structure
    • Competition
    • Global stability
    • Periodic solution

    Cite this

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    abstract = "A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.",
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    Modelling and analysis of a competitive model with stage structure. / Xu, Rui; Chaplain, M. A. J.; Davidson, F. A.

    In: Mathematical and Computer Modelling, Vol. 41, No. 2-3, 2005, p. 159-175.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Modelling and analysis of a competitive model with stage structure

    AU - Xu, Rui

    AU - Chaplain, M. A. J.

    AU - Davidson, F. A.

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    AB - A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.

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    KW - Periodic solution

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