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Journal of Nonlinear Science

, Volume 12, Issue 6, pp 641–676 | Cite as

A Dynamical System for Plant Pattern Formation: A Rigorous Analysis

  • Atela
  • Golé
  • Hotton
Article

Summary

We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system, as well as by the structure of their bifurcation diagram. We provide a detailed study of this diagram.

Key words. Phyllotaxis, pattern formation, Fibonacci, parastichy 

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Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Atela
    • 1
  • Golé
    • 1
  • Hotton
    • 2
  1. 1.Department of Mathematics, Smith College, Northampton, MA 01063, USAUS
  2. 2.Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USAUS

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