Applications of KAM theory to population dynamics

Computer simulations have shown that several classes of population models, including the May host-parasitoid model and the Ginzburg-Taneyhill 'maternal-quality' single species population model, exhibit extremely complicated orbit structures. These structures include islands-around-islands,...

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Bibliographic Details
Published inJournal of biological dynamics Vol. 5; no. 1; pp. 44 - 63
Main Authors Gidea, Marian, Meiss, James D., Ugarcovici, Ilie, Weiss, Howard
Format Journal Article
LanguageEnglish
Published England Taylor & Francis 01.01.2011
Subjects
area preserving map
elliptic fixed point
Humans
KAM theorem
last invariant circle
Models, Biological
Periodicity
Population Dynamics
population model
reversibility
twist map
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Summary:Computer simulations have shown that several classes of population models, including the May host-parasitoid model and the Ginzburg-Taneyhill 'maternal-quality' single species population model, exhibit extremely complicated orbit structures. These structures include islands-around-islands, ad infinitum, with the smaller islands containing stable periodic points of higher period. We identify the mechanism that generates this complexity and we discuss some biological implications.
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ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2010.488301