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Symbolic dynamics of coupled map lattices
Shawn D Pethel1, Ned J Corron, Erik Bollt
1U.S. Army Aviation and Missile Command, AMSRD-AMR-WS-ST, Redstone Arsenal, Alabama 35898, USA.
Physical Review Letters
|February 21, 2006
Summary
We developed a symbolic method to simplify coupled map lattice dynamics into N-bit sequences. This approach aids in identifying system behaviors and studying pattern formation in complex coupled map lattices.
Area of Science:
- Complex Systems
- Dynamical Systems Theory
- Symbolic Dynamics
Background:
- Coupled map lattices (CMLs) exhibit complex dynamics.
- Analyzing these dynamics is crucial for understanding emergent behaviors.
- Existing methods may not fully capture the intricate patterns in CMLs.
Purpose of the Study:
- To introduce a novel symbolic method for analyzing CML dynamics.
- To demonstrate the completeness of this symbolic representation.
- To facilitate the study of pattern formation in CMLs.
Main Methods:
- Representing CML dynamics as sequences of N-bit symbols.
- Utilizing concepts from symbolic dynamics of one-dimensional chaotic maps.
- Applying generating partitions, Gray orderings, and kneading sequences.
Main Results:
- A complete symbolic description of CML dynamics is achieved.
- The method allows identification of fixed points, periodic orbits, and dense orbits.
- An efficient representation for studying pattern formation is provided.
Conclusions:
- The proposed symbolic method offers a powerful tool for CML analysis.
- It provides a unified framework connecting CMLs to well-established symbolic dynamics.
- The method is exemplified using coupled quadratic maps.
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