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Inferring Lévy walks from curved trajectories: A rescaling method.

R M Tromer1, M B Barbosa1,2, F Bartumeus2,3

  • 1Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal-RN, 59078-970, Brazil.

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Summary

This study introduces a novel projection method to detect Lévy walks in complex 2D and 3D trajectories. The technique successfully distinguishes Lévy walks from correlated random walks, even with path curvature and noise.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Analyzing anomalous diffusion and transport relies on accurate trajectory data analysis.
  • Inferring Lévy walk patterns in 2D and 3D is challenging due to path curvature, unlike in 1D.

Purpose of the Study:

  • To evaluate a 1D projection method for detecting 2D Lévy walks with curvature.
  • To differentiate between Lévy walks and Markovian correlated random walks with identical step and angle distributions.

Main Methods:

  • Applied a 1D projection method to 2D and 3D trajectory data.
  • Introduced data rescaling and coarse-graining to the projection method.
  • Analyzed the probability density function (pdf) of travel distances for fat-tailed signatures.

Main Results:

  • The rescaled projection method reveals a fat tail in the pdf for Lévy walks, distinguishing them from correlated random walks.
  • This method effectively identifies Lévy walks even in the presence of noise from path curvature.
  • Correlated random walks do not exhibit the fat-tailed signature under the same analysis.

Conclusions:

  • The enhanced projection method reliably detects Lévy walks in complex, curved trajectories.
  • This protocol offers a valuable tool for analyzing animal movement and other real-world transport phenomena.
  • The findings contribute to ongoing debates about Lévy walk prevalence in natural systems.