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A universal scaling law in complex systems

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Listed:
  • Fang, Qiannan
  • Cai, Xiaohua
  • Zhou, Lei
  • Ren, Zhuoming
  • Weng, Tongfeng

Abstract

We restudy complex systems from multiscale perspective via algebraic topological analysis. By constructing networks from coarse-grained time series, we show that their topological structure in the resulting networks exhibits a universal scaling characteristic. Specifically, we find that a clear power-law behavior emerges between the number of higher-order cliques and the temporal scale in chaotic models and fractional Brownian motion. Interestingly, their associated scaling exponents present a monotonic growth pattern. This monotonic pattern is further demonstrated across stride interval fluctuations, sea clutter amplitude, bird flight speed and XRP price. Our work for the first time reveals a universal scaling law in shaping seemingly distinct complex systems.

Suggested Citation

  • Fang, Qiannan & Cai, Xiaohua & Zhou, Lei & Ren, Zhuoming & Weng, Tongfeng, 2025. "A universal scaling law in complex systems," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925011968
    DOI: 10.1016/j.chaos.2025.117183
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    References listed on IDEAS

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