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    Size-structured competition models with periodic coefficients.

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    Author
    Alameddine, Mona Fouad.
    Issue Date
    1993
    Keywords
    Dissertations, Academic.
    Mathematics.
    Committee Chair
    Cushing, James M.
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    A system of ordinary differential equations describing the dynamics of two size structured species competing for a single unstructured resource in a chemostat is derived, under the assumption that all physiological parameters of the species are periodic functions of time. The existence of nontrivial periodic solutions of those systems is considered. Under fairly general conditions, using global bifurcation techniques, we show that a continuum of solutions bifurcate from a noncritical periodic solution of the reduced system. The positivity and stability of the bifurcating branch solutions are studied. Application to mathematical ecology is given by considering several specific cases where all system parameters are constant except some selected parameters which are taken to be small amplitude oscillations around a positive mean value. Those specific cases are studied both analytically and numerically. It is also shown, that the average size of individuals of each species is governed by a nonautonomous logistic equation whose solution under fairly general conditions approaches the unique positive periodic solution of the classical periodic logistic equation. The relationship between competitive success, coexisting species and species size is discussed. Some biological considerations are addressed including the Size-Efficiency-Hypothesis, the effects of seasonality and food limitation on the coexistence of both species.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Applied Mathematics
    Graduate College
    Degree Grantor
    University of Arizona
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    Dissertations

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