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Spatial recurrence plots.

D B Vasconcelos1, S R Lopes, R L Viana

  • 1Departamento de Física, Universidade Federal do Paraná, Curitiba, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 29, 2006
PubMed
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We introduce spatial recurrence plots (SRPs) for analyzing spatial patterns. This method quantifies roughness and disorder, aiding the study of complex systems and synchronization domains.

Area of Science:

  • Complex Systems Analysis
  • Spatial Pattern Quantification
  • Nonlinear Dynamics

Background:

  • Recurrence plots are established for time series analysis.
  • Quantitative analysis of spatial pattern roughness and disorder is challenging.
  • Coupled map lattices generate complex spatial patterns.

Purpose of the Study:

  • To extend recurrence plot concepts for spatial pattern analysis.
  • To introduce spatial recurrence plots (SRPs) for quantitative analysis.
  • To develop complexity measures for spatial patterns.

Main Methods:

  • Developing spatial recurrence plots (SRPs) as a graphical representation.
  • Utilizing the pointwise correlation matrix for spatial return plots.
  • Applying SRPs to complex patterns from coupled map lattices.

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Main Results:

  • SRPs provide a quantitative method for analyzing spatial pattern roughness and disorder.
  • Complexity measures based on SRPs systematically investigate spatially coherent structures.
  • Synchronization domains in lattice profiles can be effectively studied using SRPs.

Conclusions:

  • SRPs offer a novel approach for characterizing spatial patterns.
  • The proposed complexity measures are valuable for understanding complex systems.
  • This technique has broad applicability, including surface roughness analysis.