A PRACTICAL METHOD FOR CALCULATING LARGEST LYAPUNOV EXPONENTS FROM SMALL DATA SETS
A PRACTICAL METHOD FOR CALCULATING LARGEST LYAPUNOV EXPONENTS FROM SMALL DATA SETS
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DOI：
10.1016/0167-2789(93)90009-p
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发表时间：
1993-05-15
影响因子：
4
通讯作者：
DE LUCA, CJ
中科院分区：
文献类型：
--
作者：
ROSENSTEIN, MT;COLLINS, JJ;DE LUCA, CJ
检测混沌在动力系统中的存在是一个重要的问题，通过测量最大李雅普诺夫指数来解决。李雅普诺夫指数量化了初始封闭状态空间轨迹的指数散度，并估计了系统中的混沌量。我们提出了一种从实验时间序列中计算最大李雅普诺夫指数的新方法。该方法直接遵循最大李雅普诺夫指数的定义，并且由于它利用了所有可用的数据而准确。我们证明了该算法快速，易于实现，并且对以下数量的变化具有鲁棒性：嵌入维数，数据集大小，重构延迟和噪声水平。此外，可以使用该算法同时计算相关维数。因此，一个计算序列将产生对混沌水平和系统复杂性的估计。
Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest Lyapunov exponent. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. We present a new method for calculating the largest Lyapunov exponent from an experimental time series. The method follows directly from the definition of the largest Lyapunov exponent and is accurate because it takes advantage of all the available data. We show that the algorithm is fast, easy to implement, and robust to changes in the following quantities: embedding dimension, size of data set, reconstruction delay, and noise level. Furthermore, one may use the algorithm to calculate simultaneously the correlation dimension. Thus, one sequence of computations will yield an estimate of both the level of chaos and the system complexity.