Estimating optimal partitions for stochastic complex systems
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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.
KeywordsAkaike Information Criterion European Physical Journal Special Topic Topological Entropy Deterministic System Optimal Partition
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- 21.J. MacQueen, In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, USA, 1967), p. 281Google Scholar
- 23.T. Nakamura, Ph.D. thesis, School of Mathematics & Statistics, The University of Western Australia, 2003Google Scholar
- 24.K.P. Burnham, D.R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (Springer, New York, USA, 2002)Google Scholar