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Hopf Bifurcation in the Two Locus Genetic Model
Ethan Akin

Memoirs of the American Mathematical Society
1983; 190 pp; softcover
Volume: 44
ISBN-10: 0-8218-2284-5
ISBN-13: 978-0-8218-2284-5
List Price: US$29
Individual Members: US$17.40
Institutional Members: US$23.20
Order Code: MEMO/44/284
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"The technical results are surrounded by enough narrative to make the book readable without total immersion, in agreeable contrast to some earlier texts on topological dynamics. The many exercises contain some of the details of proofs, as well as pointers to other areas and a number of individual gems. This will be a useful book for readers of a topological bent already familiar with the basics of dynamical systems theory; it contains much fundamental material, tells a unified story, and has appeared at the right time."

-- Bulletin of the London Mathematical Society

Table of Contents

I. Cycles in simple genetic systems
  • The space of selection matrices
  • Eigenvalues, eigenvectors and linear differential equations
  • Nonlinear equilibria and Hopf bifurcations
  • The Hopf bifurcation locus
  • Parametrization of \(\Sigma_H\)
  • Symmetries
  • Concluding remarks
II. Parametric description of the Hopf locus
  • Linear maps, bilinear forms and matrices
  • Coordinates and the cylindrical frame
  • Linearizations and Hessians
  • The parametrization
  • Symmetric cases
  • Asymptotic estimates
III. Programs and examples
  • The general program
  • The symmetric program
  • Sample computations
  • Bibliography
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