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A generalized high-order correlation dimension for strange attractors

Author

Listed:
  • Weng, Tongfeng
  • Wu, Minze
  • Feng, Shiyuan
  • Chen, Xiaolu
  • Ren, Zhuoming
  • Liu, Runran
  • Small, Michael

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.

Suggested Citation

  • Weng, Tongfeng & Wu, Minze & Feng, Shiyuan & Chen, Xiaolu & Ren, Zhuoming & Liu, Runran & Small, Michael, 2025. "A generalized high-order correlation dimension for strange attractors," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002036
    DOI: 10.1016/j.chaos.2025.116190
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