A generalized high-order correlation dimension for strange attractors

Tongfeng Weng, Minze Wu, Shiyuan Feng, Xiaolu Chen, Zhuoming Ren, Runran Liu and Michael Small

Chaos, Solitons & Fractals, 2025, vol. 194, issue C

Abstract: Correlation dimension is a well-known measurement for characterizing strange attractors but only exploring low-order correlation in complex orbit structure. We propose a generalized correlation dimension of strange attractors based on algebraic topology. By mapping a strange attractor into consecutive graphs under different similarity scales, we identify a power law relation between the number of a specific order of clique and the similarity scale, defining a finite algebraic exponent. Interestingly, we find that the algebraic exponent follows a linear growth pattern as a function of the order of clique. We demonstrate that this is a universal principle governing topological structure of strange attractors.

Keywords: Strange attractor; Correlation dimension; Algebraic topology; Clique (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002036

DOI: 10.1016/j.chaos.2025.116190

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