Influence of the singular manifold of nonobservable states in reconstructing chaotic attractors
Influence of the singular manifold of nonobservable states in reconstructing chaotic attractors
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DOI：
10.1103/physreve.86.026205
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发表时间：
2012-08-14
影响因子：
2.4
通讯作者：
Letellier, Christophe
中科院分区：
文献类型：
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作者：
Frunzete, Madalin;Barbot, Jean-Pierre;Letellier, Christophe
已知给定系统的重构相图强烈依赖于可观测量的选择。特别是，从时间序列中获得全局模型的能力强烈依赖于测量变量提供的可观测性。这种依赖性源于（i）奇异可观测性流形M-s（obs）的存在，其中R-m和重构空间之间的坐标变换未定义，以及（ii）轨迹访问M-s（obs）的邻域U-Msobs的频率。为了阐明这些方面对可观测性系数的贡献，我们引入了访问M-s（obs）的概率和在U-Msobs中花费的相对时间来构造一个新的系数。结合先前引入的符号可观测性系数[Letellier and Aguirre，Phys. Rev. E 79，066210（2009）]（仅考虑M-s（obs）的存在），这个新系数有助于确定M-s（obs）相对于吸引子的位置在相图重建和任何分析技术中所扮演的特定角色。
It is known that the reconstructed phase portrait of a given system strongly depends on the choice of the observable. In particular, the ability to obtain a global model from a time series strongly depends on the observability provided by the measured variable. Such a dependency results from (i) the existence of a singular observability manifold, M-s(obs), for which the coordinate transformation between R-m and the reconstructed space is not defined and (ii) how often the trajectory visits the neighborhood U-Msobs of M-s(obs). In order to clarify how these aspects contribute to the observability coefficients, we introduce the probability of visits of M-s(obs) and the relative time spent in U-Msobs to construct a new coefficient. Combined with the symbolic observability coefficients previously introduced [Letellier and Aguirre, Phys. Rev. E 79, 066210 (2009)] (only taking into account the existence of M-s(obs)), this new coefficient helps to determine the specific role played by the location of M-s(obs) with respect to the attractor, in phase portrait reconstruction and in any analysis technique.