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Related Experiment Videos

Dynamics of spatial averages.

Leonid Bunimovich1, Miaohua Jiang

  • 1School of Mathematics and Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30332-0160.

Chaos (Woodbury, N.Y.)
|March 1, 1997
PubMed
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Spatial averages in extended dynamical systems exhibit diverse behaviors like constant, periodic, or non-periodic patterns. Fluctuations arise from subsystem transitivity and asymmetry, impacting overall system dynamics.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Spatially extended dynamical systems are fundamental in modeling phenomena across various scientific disciplines.
  • Understanding the behavior of spatial averages is crucial for characterizing macroscopic properties.
  • Previous studies often focused on local dynamics, with less emphasis on the collective behavior of spatial averages.

Purpose of the Study:

  • To investigate the dynamic behaviors of spatial averages in lattice dynamical systems.
  • To identify the factors contributing to the variability observed in spatial averages.
  • To provide a theoretical framework for understanding fluctuations in extended systems.

Main Methods:

  • Analysis of various lattice dynamical systems.

Related Experiment Videos

  • Mathematical modeling of spatial averaging.
  • Examination of subsystem transitivity and symmetry properties.

    • Main Results:

    • Demonstrated that spatial averages can be asymptotically constant, periodic, or non-periodic.
    • Identified transitivity and lack of symmetry in local subsystem dynamics as key drivers of spatial average fluctuations.
    • Provided concrete examples of lattice systems exhibiting these diverse average behaviors.

    Conclusions:

    • The dynamics of spatial averages are complex and depend on the properties of local subsystems.
    • Transitivity and asymmetry are critical elements influencing the stability and predictability of extended systems.
    • This study offers insights into the macroscopic behavior of complex systems based on their microscopic interactions.