Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays

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

    Research output: Contribution to journalArticle

    21 Citations (Scopus)

    Abstract

    In this paper, we first investigate a stage-structured competitive model with time delays, harvesting, and nonlocal spatial effect. By using an iterative technique recently developed by Wu and Zou (Wu J, Zou X. Travelling wave fronts of reaction–diffusion systems with delay. J Dynam Differen Equat 2001;13:651–87), sufficient conditions are established for the existence of travelling front solution connecting the two boundary equilibria in the case when there is no positive equilibrium. The travelling wave front corresponds to an invasion by a stronger species which drives the weaker species to extinction. Secondly, we consider a stage-structured competitive model with time delays and nonlocal spatial effect when the domain is finite. We prove the global stability of each of the nonnegative equilibria and demonstrate that the more complex model studied here admits three possible long term behaviors: coexistence, bistability and dominance as is the case for the standard Lotka–Voltera competitive model.
    Original languageEnglish
    Pages (from-to)974-992
    Number of pages19
    JournalChaos, Solitons & Fractals
    Volume30
    Issue number4
    DOIs
    Publication statusPublished - Nov 2006

    Keywords

    • Travelling wavefronts
    • Global convergence

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