Fast numerical test of hyperbolic chaos.
Fast numerical test of hyperbolic chaos.
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双曲混沌的快速数值测试。
DOI：
10.1103/physreve.85.015203
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
P. V. Kuptsov
中科院分区：
文献类型：
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作者：
P. V. Kuptsov
提出了一种检验混沌动力学双曲性的有效数值方法。该方法采用协变李雅普诺夫向量算法的思想，但避免了显式计算。其结果是一个分布的特征值是有界的单位区间内，其零表示之间的切线膨胀和收缩的子空间。要进行测试，必须解决几个副本的方程的无穷小扰动，其数量等于总和的数量的积极和零李雅普诺夫指数。由于该数目通常远小于全相空间维数，该方法为数值双曲性检验提供了一种快速、节省内存的方法。
An effective numerical method for testing the hyperbolicity of chaotic dynamics is suggested. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a distribution of a characteristic value which is bounded within the unit interval and whose zero indicates a tangency between expanding and contracting subspaces. To perform the test one has to solve several copies of equations for infinitesimal perturbations whose number is equal to the sum of numbers of positive and zero Lyapunov exponents. Since this number is normally much less than the full phase space dimension, this method provides a fast and memory saving way for numerical hyperbolicity testing.