Marian Gidea, James D. Meiss, Ilie Ugarcovici, and Howard Weiss
Applications of KAM Theory to Population Dynamics
(1380K, pdf)

ABSTRACT.  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.