Covariant Lyapunov vectors from reconstructed dynamics: the geometry behind true and spurious Lyapunov exponents.
Covariant Lyapunov vectors from reconstructed dynamics: the geometry behind true and spurious Lyapunov exponents.
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DOI：
10.1103/physrevlett.109.244101
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发表时间：
2012-12
影响因子：
8.6
通讯作者：
Hong-liu Yang;G. Radons;H. Kantz
中科院分区：
文献类型：
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作者：
Hong-liu Yang;G. Radons;H. Kantz
在时间序列的Lyapunov指数估计中，由于必要的嵌入过程，会出现虚假的Lyapunov指数。区分真伪指数是一个尚未令人满意地解决的基本问题。在这封信中，我们用解析和数值的方法证明了与真指数相关的协变Lyapunov向量位于重构吸引子的切线空间中。因此，我们使用协变Lyapunov向量与重构吸引子的切线空间之间的夹角来识别真实的Lyapunov指数。我们的方法的有效性，也适用于噪声情况，通过对模型系统的数据和核磁共振激光实验的应用得到了证明。
The estimation of Lyapunov exponents from time series suffers from the appearance of spurious Lyapunov exponents due to the necessary embedding procedure. Separating true from spurious exponents poses a fundamental problem which is not yet solved satisfactorily. We show, in this Letter, analytically and numerically that covariant Lyapunov vectors associated with true exponents lie in the tangent space of the reconstructed attractor. Therefore, we use the angle between the covariant Lyapunov vectors and the tangent space of the reconstructed attractor to identify the true Lyapunov exponents. The usefulness of our method, also for noisy situations, is demonstrated by applications to data from model systems and a NMR laser experiment.