A computational approach to Conley's decomposition theorem
A computational approach to Conley's decomposition theorem
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DOI：
10.1115/1.2338651
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发表时间：
2006-10-01
影响因子：
2
通讯作者：
Kalies, William D.
中科院分区：
文献类型：
--
作者：
Ban, Hyunju;Kalies, William D.
背景资料。由连续映射产生的离散动力学可以由相空间离散化上的所有适当的多值映射来组合表示，例如立方体网格或三角剖分。接近的方法。我们描述了计算组合多值映射的动力结构的显式算法。结果。我们给出了计算复杂性的界和数值例子。具体地说，我们着重于Morse分解的吸引子-排斥子对和Lyapunov函数的计算。结论。计算的离散Lyapunov函数是弱Lyapunov函数，并且很好地逼近了底层映射的连续Lyapunov函数。
Background. The discrete dynamics generated by a continuous map call be represented combinatorially by all appropriate multivalued map on a discretization of the phase space such as a cubical grid or triangulation. Method of approach. We describe explicit algorithms for computing dynamical structures for the combinatorial multivalued maps. Results. We provide computational complexity bounds and numerical examples. Specifically we focus on the computation attractor-repeller pairs and Lyapunov functions for Morse decompositions. Conclusions. The computed discrete Lyapunov functions are weak Lyapunov functions and well-approximate a continuous Lyapunov function for the under-lying map.