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Coupled map models for chaos in extended systems.

M. S. Bourzutschky1, M. C. Cross

  • 1Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125.

Chaos (Woodbury, N.Y.)
|April 1, 1992
PubMed
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This study introduces coupled maps with conserved quantities as models for chaos in extended systems. Numerical experiments explore thermodynamic properties and derive a Langevin equation for a one-dimensional system.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Nonlinear Dynamics

Background:

  • Extended systems often exhibit complex behaviors, including chaos.
  • Conserved quantities play a crucial role in understanding the dynamics of such systems.
  • Modeling chaos in extended systems requires appropriate theoretical frameworks.

Purpose of the Study:

  • To introduce coupled maps with conserved quantities as models for chaos in extended systems.
  • To investigate the long-wavelength limit of a one-dimensional example in detail.
  • To explore the potential thermodynamic properties of these chaotic systems.

Main Methods:

  • Derivation of a Langevin equation for the one-dimensional system.
  • Discussion of the applicability of the fluctuation-dissipation theorem.

Related Experiment Videos

  • Conducting numerical experiments to analyze system properties.

    • Main Results:

    • Coupled maps with conserved quantities are presented as viable models for chaos.
    • A Langevin equation is successfully derived for the long-wavelength limit.
    • Numerical investigations provide insights into potential thermodynamic properties.

    Conclusions:

    • The developed models offer a framework for studying chaos in extended systems.
    • The derived Langevin equation and fluctuation-dissipation theorem analysis are key contributions.
    • Further numerical experiments are suggested for a deeper understanding of thermodynamic properties.