A universal scaling law in complex systems

Qiannan Fang, Xiaohua Cai, Lei Zhou, Zhuoming Ren and Tongfeng Weng

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

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.

Keywords: Multiscale topological analysis; Complex systems time series; Visibility graph; Clique (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925011968

DOI: 10.1016/j.chaos.2025.117183

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