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Local estimates for entropy densities in coupled map lattices
1Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, D 01187 Dresden, Germany.
Physical Review Letters
|October 4, 2000
Summary
We developed a new method to estimate entropy density in complex systems using local data. This approach helps understand the system
Area of Science:
- Complex systems
- Nonlinear dynamics
- Information theory
Background:
- Coupled map lattices (CML) are complex systems exhibiting rich dynamics.
- Estimating entropy density in such systems is crucial for understanding their behavior.
- Traditional methods often require global information, which is not always accessible.
Purpose of the Study:
- To present a novel method for deriving an upper bound for entropy density in CML.
- To enable entropy estimation from local observations only.
- To identify the local character of the underlying equations of motion.
Main Methods:
- Utilizing a combined time delay and spatial embedding technique.
- Applying this embedding to reconstruct the system's dynamics from local data.
- Employing the correlation integral for approximate entropy density estimation.
Main Results:
- Successfully derived an upper bound for entropy density.
- Demonstrated the feasibility of estimating entropy from local observations.
- The embedding technique effectively captures the local dynamics.
Conclusions:
- The proposed method provides a practical approach to quantify the complexity of CML.
- Local observations are sufficient for estimating key thermodynamic properties like entropy density.
- This work advances the understanding of information processing in spatially extended systems.
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