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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

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Published on: February 9, 2017

Deconstructing spatiotemporal chaos using local symbolic dynamics.

Shawn D Pethel1, Ned J Corron, Erik Bollt

  • 1AMSRD-AMR-WS-ST, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898, USA.

Physical Review Letters
|February 1, 2008
PubMed
Summary
This summary is machine-generated.

Global symbolic dynamics in coupled map lattices can be accurately predicted by simplified local models, especially with weaker coupling. This research demonstrates robust approximation and control of complex spatiotemporal chaos using these reduced models.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems analysis
  • Computational physics

Background:

  • Coupled map lattices exhibit complex spatiotemporal chaos.
  • Understanding the global dynamics of such systems is computationally challenging.
  • Local models offer a potential simplification for analyzing complex systems.

Purpose of the Study:

  • To investigate the effectiveness of local symbolic models in approximating global dynamics of diffusively coupled map lattices.
  • To provide rigorous analysis of model accuracy across various coupling strengths and local model sizes.
  • To demonstrate practical applications in data analysis and chaos control.

Main Methods:

  • Symbolic dynamics analysis
  • Development and application of local symbolic models
  • Interval analysis for rigorous bounding of approximation errors
  • Data-driven extraction of local models
  • Control of spatiotemporal chaos using local models

Main Results:

  • Global symbolic dynamics are well approximated by small local models for weak to moderate coupling.
  • Rigorous bounds on approximation accuracy were established using interval analysis.
  • Successful extraction of local symbolic models from data was demonstrated.
  • Effective control of spatiotemporal chaos was achieved via local model strategies.

Conclusions:

  • Simplified local models provide accurate approximations of complex coupled map lattice dynamics.
  • Local symbolic dynamics offer a powerful framework for analyzing, predicting, and controlling spatiotemporal chaos.
  • The findings have implications for understanding and managing complex systems in various scientific domains.