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Related Experiment Videos

Pattern formation in diffusive-advective coupled map lattices.

Pedro G Lind1, João Corte-Real, Jason A C Gallas

  • 1Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study explores pattern formation in coupled map lattices with advection, revealing how it alters evolution and induces synchronization. We also present an algorithm for classifying patterns and measuring wave velocities.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Computational Physics

Background:

  • Coupled map lattices (CMLs) are widely used to model complex spatio-temporal phenomena.
  • Understanding pattern formation and evolution in CMLs is crucial for various scientific disciplines.
  • Previous studies primarily focused on diffusive and nonlinear terms, with limited exploration of advection's role.

Purpose of the Study:

  • To investigate the impact of advection on pattern formation and evolution in coupled map lattices.
  • To classify the emergent patterns into distinct categories based on their dynamics.
  • To determine the relative frequencies of these patterns as a function of model parameters.

Main Methods:

  • Incorporation of an advection term alongside the diffusive term in the CML model.

Related Experiment Videos

  • Systematic variation of model parameters: diffusion, advection, local nonlinearity, and lattice size.
  • Development of a practical algorithm for classifying pattern evolutions and measuring traveling wave velocities.

    • Main Results:

    • Identified five distinct classes of patterns: three periodic (static and traveling waves) and two nonperiodic.
    • Demonstrated that advection significantly alters pattern evolution, including inducing synchronization in chaotic patterns.
    • Quantified the relative frequencies of pattern classes across the parameter space.

    Conclusions:

    • Advection is a critical factor influencing pattern dynamics in coupled map lattices.
    • The presence of advection can lead to the emergence of ordered behavior from chaotic states.
    • The developed classification algorithm provides a robust tool for analyzing complex spatio-temporal systems.