A dynamical system for plant pattern formation:: A rigorous analysis
A dynamical system for plant pattern formation:: A rigorous analysis
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DOI：
10.1007/s00332-002-0513-1
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发表时间：
2002-11-01
影响因子：
3
通讯作者：
Hotton, S
中科院分区：
文献类型：
--
作者：
Atela, P;Golé, C;Hotton, S
我们提出了一个严格的数学分析的离散动力系统建模植物格局的形成。在这个模型中，基于物理学家Douady和Couder的工作，不动点是植物中经常出现的螺旋或螺旋晶格。斐波那契序列在可见螺旋数中的频繁出现可以通过该系统中不动点的稳定性以及它们的分叉图的结构来解释。我们提供了这个图的详细研究。
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.