A Dynamical System for Plant Pattern Formation: A Rigorous Analysis |
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| Authors: | Atela Golé and Hotton |
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| Institution: | (1) Department of Mathematics, Smith College, Northampton, MA 01063, USA, US;(2) Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USA, US |
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| Abstract: | 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. |
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| Keywords: | , Phyllotaxis, pattern formation, Fibonacci, parastichy |
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