Reversing invasion in bistable systems

Ebrahim O. Alzahrani, Fordyce A. Davidson, Niall Dodds

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    In this paper, we discuss a class of bistable reaction-diffusion systems used to model the competitive interaction of two species. The interactions are assumed to be of classic "Lotka-Volterra" type and we will consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems, we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three "zones of response". In the central zone, varying the motility can slow, halt and reverse invasion. However, in the two outer zones, the direction of invasion is independent of the relative motility and is entirely determined by the relative competitive strengths. Furthermore, we conjecture that for a large class of competition models of the type studied here, the wave speed is an increasing function of the relative motility.
    Original languageEnglish
    Pages (from-to)1101-1124
    Number of pages24
    JournalJournal of Mathematical Biology
    Volume65
    Issue number6-7
    DOIs
    Publication statusPublished - Dec 2012

    Fingerprint

    Bistable System
    Motility
    Invasion
    Competition Model
    Wave Speed
    Population Dynamics
    Population dynamics
    Lotka-Volterra
    Increasing Functions
    population dynamics
    Reaction-diffusion System
    Interaction
    Reverse
    Class
    Direction compound

    Cite this

    Alzahrani, Ebrahim O. ; Davidson, Fordyce A. ; Dodds, Niall . / Reversing invasion in bistable systems. In: Journal of Mathematical Biology. 2012 ; Vol. 65, No. 6-7. pp. 1101-1124.
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    title = "Reversing invasion in bistable systems",
    abstract = "In this paper, we discuss a class of bistable reaction-diffusion systems used to model the competitive interaction of two species. The interactions are assumed to be of classic {"}Lotka-Volterra{"} type and we will consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems, we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three {"}zones of response{"}. In the central zone, varying the motility can slow, halt and reverse invasion. However, in the two outer zones, the direction of invasion is independent of the relative motility and is entirely determined by the relative competitive strengths. Furthermore, we conjecture that for a large class of competition models of the type studied here, the wave speed is an increasing function of the relative motility.",
    author = "Alzahrani, {Ebrahim O.} and Davidson, {Fordyce A.} and Niall Dodds",
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    Reversing invasion in bistable systems. / Alzahrani, Ebrahim O.; Davidson, Fordyce A.; Dodds, Niall .

    In: Journal of Mathematical Biology, Vol. 65, No. 6-7, 12.2012, p. 1101-1124.

    Research output: Contribution to journalArticle

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    AU - Alzahrani, Ebrahim O.

    AU - Davidson, Fordyce A.

    AU - Dodds, Niall

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    PY - 2012/12

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