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Counter-Examples about Lower- and Upper-Bounded Population Growth

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  • Jacques Demongeot
  • Jules Waku
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    Abstract

    For a unimodal growth function f having its maximum at a critical state xc, the interval bounding the population size asymptotically is usually presented as being equal to [f○2(xc), f(xc)]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f○2(xc)), f(xc)], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 12 (2005)
    Issue (Month): 4 ()
    Pages: 199-209

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    Handle: RePEc:taf:mpopst:v:12:y:2005:i:4:p:199-209

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    Related research

    Keywords: interval iteration; invariant domain; population dynamics; growth model; Verhulst model; Ricker model;

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