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Synchronization and coherence in thermodynamic coupled map lattices with intermediate-range coupling.

P M Gade1, C K Hu

  • 1Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan. pgade@phys.sinica.edu.tw

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study investigates coupled map lattices (CMLs) with intermediate-range interactions. Synchronization depends on the fraction of coupled sites, not their total number, in the thermodynamic limit.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Intermediate-range interactions are a natural feature in some spatially extended physical systems.
  • Coupled Map Lattices (CMLs) provide a framework for studying complex dynamics in such systems.
  • Understanding synchronization phenomena is crucial for predicting system behavior.

Purpose of the Study:

  • To investigate the synchronization properties of CMLs with intermediate-range coupling.
  • To derive analytic conditions for synchronization in these systems.
  • To determine the key parameters governing synchronization and coherence in the thermodynamic limit.

Main Methods:

  • Analysis of a CML model incorporating intermediate-range coupling.
  • Derivation of analytic conditions for system synchronization.

Related Experiment Videos

  • Application of the law of large numbers to the mean field.
  • Investigation of power spectrum properties in the thermodynamic limit.

    • Main Results:

    • The law of large numbers applies to the mean field when the coupling range is fixed.
    • The total normalized power in nonzero components of the mean field's power spectrum approaches zero in the thermodynamic limit.
    • Synchronization and coherence are primarily determined by the fraction of coupled sites, not their absolute number, in the thermodynamic limit.

    Conclusions:

    • The fraction of coupled sites is the critical factor for synchronization in CMLs with intermediate-range interactions, rather than the total number of coupled sites.
    • These findings offer insights into the behavior of spatially extended systems with non-local interactions.
    • The study highlights the importance of interaction range and site fraction in determining collective behavior and coherence.