How the choice of the observable may influence the analysis of nonlinear dynamical systems
How the choice of the observable may influence the analysis of nonlinear dynamical systems
复制标题
可观测量的选择如何影响非线性动力系统的分析
DOI：
10.1016/j.cnsns.2005.01.003
复制
发表时间：
2006
影响因子：
3.9
通讯作者：
J. Maquet
中科院分区：
文献类型：
--
作者：
C. Letellier;L. A. Aguirre;J. Maquet
为了研究非线性动力系统而开发的大量技术开始于在d维空间中嵌入标量时间序列，该标量时间序列位于m维对象上，d>m。在一般情况下，达到的主要结果是有效的，无论观察选择。然而，在许多实际情况下，观察的选择确实影响我们从嵌入吸引子中提取动力学信息的能力。这可能会出现在非线性动力学的标准问题，如模型建立，控制理论和同步。在某种程度上，成功的难易程度将取决于可观测量的选择，因为它与动力学的可观测性有关。通过对Rössler系统的研究，我们证明了可观测性矩阵与原始相空间和由可观测量诱导的微分嵌入之间的映射有关。本文研究了非线性系统的能观矩阵的一种形式，它比以往所用的能观矩阵形式更具有一般性。还提到了可控性问题。
A great number of techniques developed for studying nonlinear dynamical systems start with the embedding, in a d-dimensional space, of a scalar time series, lying on an m-dimensional object, d>m. In general, the main results reached at are valid regardless of the observable chosen. In a number of practical situations, however, the choice of the observable does influence our ability to extract dynamical information from the embedded attractor. This may arise in standard problems in nonlinear dynamics such as model building, control theory and synchronization. To some degree, ease of success will thus depend on the choice of observable simply because it is related to the observability of the dynamics. Investigating the Rössler system, we show that the observability matrix is related to the map between the original phase space and the differential embedding induced by the observable. This paper investigates a form for the observability matrix for nonlinear system which is more general than the previous one used. The problem of controllability is also mentioned.