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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
Summary
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.
- 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.