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Characterizing systems by multi-scale structural complexity

Author

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  • Wang, Ping
  • Gu, Changgui
  • Yang, Huijie
  • Wang, Haiying
  • Moore, Jack Murdoch

Abstract

Complexity is one of the most fundamental criteria by which people distinguish different types of systems. However, the concept of complexity remains difficult to quantify objectively. In this article, we exploit recent advances in measuring the complexity of visual images to develop a multi-scale structural complexity method for characterizing system complexity based solely on a scalar time series. Moreover, we develop a method based on scatter plots and correlation to provide visual insight into system characteristics. This method can accurately reflect the dynamical characteristics of the system as a whole. In addition, it can identify the local complexity of a system at different scales as well as indicate how the complexity of the system changes with scale. Finally, we discovered that the ratio of local complexity to total complexity varied strikingly with system type (including continuous systems, discrete systems, and empirical system), which allowed us to distinguish between them. In summary, our methods provide new insights into the multi-scale structural complexity of a system based simply on a scalar time series.

Suggested Citation

  • Wang, Ping & Gu, Changgui & Yang, Huijie & Wang, Haiying & Moore, Jack Murdoch, 2023. "Characterizing systems by multi-scale structural complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    • Handle: RePEc:eee:phsmap:v:609:y:2023:i:c:s0378437122009165
    DOI: 10.1016/j.physa.2022.128358
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    References listed on IDEAS

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    1. Gaetano Valenza & Luca Citi & Riccardo Barbieri, 2014. "Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-17, August.
    2. Yu, Jinwei & Xie, Wei & Zhong, Zhenyu & Wang, Huan, 2022. "Image encryption algorithm based on hyperchaotic system and a new DNA sequence operation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. David H. Wolpert & William G. Macready, 1997. "Self-Dissimilarity: An Empirical Measure of Complexity," Working Papers 97-12-087, Santa Fe Institute.
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    Cited by:

    1. Wang, Ping & Gu, Changgui & Yang, Huijie & Wang, Haiying, 2024. "Identify causality by multi-scale structural complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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