Hopf Bifurcation in the Two Locus Genetic Model

Ethan Akin

ม.ค. 1983 · American Mathematical Society: Memoirs of the American Mathematical Society หนังสือเล่มที่ 284 · American Mathematical Soc.

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Hopf bifurcations occur in the class of simple genetic models for the combined effect of selection and recombination. The demonstration of cycling in such models is biologically unexpected. To study this phenomenon we describe the locus of positions at which Hopf bifurcation occurs in the two-locus-two-allele model. The description is given by an explicit, computable parametrization which can be used to generate all possible examples. Asymptotic estimates show that limit cycles can occur.