The European Physical Journal Special Topics

, Volume 222, Issue 2, pp 303–315 | Cite as

Estimating optimal partitions for stochastic complex systems

Regular Article Theoretical Aspects I: Concepts, Structural Results and Methods


Partitions provide simple symbolic representations for complex systems. For a deterministic system, a generating partition establishes one-to-one correspondence between an orbit and the infinite symbolic sequence generated by the partition. For a stochastic system, however, a generating partition does not exist. In this paper, we propose a method to obtain a partition that best specifies the locations of points for a time series generated from a stochastic system by using the corresponding symbolic sequence under a constraint of an information rate. When the length of the substrings is limited with a finite length, the method coincides with that for estimating a generating partition from a time series generated from a deterministic system. The two real datasets analyzed in Kennel and Buhl, Phys. Rev. Lett. 91, 084102 (2003), are reanalyzed with the proposed method to understand their underlying dynamics intuitively.


Akaike Information Criterion European Physical Journal Special Topic Topological Entropy Deterministic System Optimal Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Institute of Industrial Science, University of TokyoTokyoJapan

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