Eur. Phys. J. Special Topics 222, 303-315 (2013)
https://doi.org/10.1140/epjst/e2013-01843-x

Regular Article

Estimating optimal partitions for stochastic complex systems

Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

^a e-mail: yoshito@sat.t.u-tokyo.ac.jp

Received: 27 March 2013
Revised: 25 April 2013
Published online: 25 June 2013

Abstract

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.