Journal of Nonlinear Science
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.
Fibonacci, Parastichy, Pattern formation, Phyllotaxis
© the authors
Atela, Pau; Golé, Christophe; and Hotton, S., "A Dynamical System for Plant Pattern Formation: A Rigorous Analysis" (2003). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.