LYAPUNOV EXPONENTS FROM OBSERVED TIME-SERIES
LYAPUNOV EXPONENTS FROM OBSERVED TIME-SERIES
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DOI：
10.1103/physrevlett.65.1523
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发表时间：
1990-09-24
影响因子：
8.6
通讯作者：
ABARBANEL, HDI
中科院分区：
文献类型：
--
作者：
BRYANT, P;BROWN, R;ABARBANEL, HDI
我们研究准确确定时间序列的李雅普诺夫指数的问题。我们发现使用具有高阶泰勒级数的局部映射比之前所做的线性映射更有利。我们针对 Ikeda 映射和 Lorenz 系统演示了此过程。我们提出了通过分析数据集奇点和确定李雅普诺夫方向向量来识别虚假指数的方法。还研究了存在噪声时虚假指数的行为，发现其与真实指数的行为不同。
We examine the question of accurately determining Lyapunov exponents for a time series. We find that it is advantageous to use local mappings with higher-order Taylor series, rather than linear maps as done earlier. We demonstrate this procedure for the Ikeda map and the Lorenz system. We present methods for identifying spurious exponents by analyzing data-set singularities and by determining the Lyapunov direction vectors. The behavior of spurious exponents in the presence of noise is also investigated, and found to be different from that of the true exponents.