A dynamical system for plant pattern formation:: A rigorous analysis

被引：46

作者：

Atela, P ^{[1
]}

Golé, C

Hotton, S

机构：

[1] Smith Coll, Dept Math, Northampton, MA 01063 USA

[2] Miami Univ, Dept Math & Stat, Oxford, OH 45056 USA

来源：

JOURNAL OF NONLINEAR SCIENCE | 2002年 / 12卷 / 06期

关键词：

phyllotaxis; pattern formation; Fibonacci; parastichy;

D O I：

10.1007/s00332-002-0513-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：641 / 676

页数：36

共 37 条

[1] MODEL OF CONTACT PRESSURE IN PHYLLOTAXIS [J].