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Multifractal signatures of complexity matching.

Didier Delignières1, Zainy M H Almurad2,3, Clément Roume2

  • 1EA 2991, Euromov, University of Montpellier, 700 avenue du Pic Saint Loup, 34090, Montpellier, France. didier.delignieres@umontpellier.fr.

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Complexity matching describes how coupled systems synchronize across scales. This study introduces a new method to differentiate genuine complexity matching from local adjustments in system interactions.

Keywords:
Complexity matchingCoordinationMultifractalsSynchronization

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Area of Science:

  • Complex systems science
  • Dynamical systems theory
  • Human motor control

Background:

  • The complexity matching effect proposes synchronization arises from multi-scale interactions.
  • This effect is observed as statistical matching between scaling exponents of coupled systems.
  • Recent studies question if observed matching reflects genuine complexity or local adjustments.

Purpose of the Study:

  • To develop and validate a novel analysis method to distinguish genuine complexity matching from local adjustments.
  • To investigate the underlying mechanisms of synchronization in coupled complex systems.

Main Methods:

  • Analysis based on the correlation between multifractal spectra across different time scales.
  • Application to diverse datasets including bimanual coordination, interpersonal coordination, and fractal metronome walking.

Main Results:

  • The proposed method successfully differentiates between genuine complexity matching and synchronization driven by local adjustments.
  • Evidence supports the distinct origins of statistical matching in complex system interactions.

Conclusions:

  • The developed method provides a robust tool for analyzing synchronization phenomena in complex systems.
  • This research clarifies the nature of complexity matching, distinguishing true system-wide synchronization from localized compensatory behaviors.