Document Type

Article

Publication Date

1-1-2003

Publication Title

Journal of Nonlinear Science

Abstract

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.

Keywords

Fibonacci, Parastichy, Pattern formation, Phyllotaxis

Volume

12

Issue

6

First Page

641

Last Page

676

DOI

10.1007/s00332-002-0513-1

ISSN

09388974

Rights

© the authors

Comments

Peer reviewed accepted manuscript.

Download

Included in

Mathematics Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.