Shrimp structure as a test bed for ordinal pattern measures.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-12-01 DOI:10.1063/5.0238632
Yong Zou, Norbert Marwan, Xiujing Han, Reik V Donner, Jürgen Kurths
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引用次数: 0

Abstract

Identifying complex periodic windows surrounded by chaos in the two or higher dimensional parameter space of certain dynamical systems is a challenging task for time series analysis based on complex network approaches. This holds particularly true for the case of shrimp structures, where different bifurcations occur when crossing different domain boundaries. The corresponding dynamics often exhibit either period-doubling when crossing the inner boundaries or, respectively, intermittency for outer boundaries. Numerically characterizing especially the period-doubling route to chaos is difficult for most existing complex network based time series analysis approaches. Here, we propose to use ordinal pattern transition networks (OPTNs) to characterize shrimp structures, making use of the fact that the transition behavior between ordinal patterns encodes additional dynamical information that is not captured by traditional ordinal measures such as permutation entropy. In particular, we compare three measures based on ordinal patterns: traditional permutation entropy εO, average amplitude fluctuations of ordinal patterns ⟨σ⟩, and OPTN out-link transition entropy εE. Our results demonstrate that among those three measures, εE performs best in distinguishing chaotic from periodic time series in terms of classification accuracy. Therefore, we conclude that transition frequencies between ordinal patterns encoded in the OPTN link weights provide complementary perspectives going beyond traditional methods of ordinal time series analysis that are solely based on pattern occurrence frequencies.

将虾结构作为序数模式测量的试验台。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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