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Comment on "Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map"
1Max Planck Institute for Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany. rklages@mpipks-dresden.mpg.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
This study clarifies deterministic diffusion in piecewise linear maps, correcting a variance in a recent paper. It highlights fractal diffusion coefficients and questions the model
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Chaos theory
Background:
- Deterministic diffusion in piecewise linear maps was recently discussed by Rajagopalan and Sabir.
- Their work utilized an approach developed by Fujisaka et al. for analyzing such systems.
Discussion:
- The authors rederived the random walk formula for the diffusion coefficient, a known exact result for Bernoulli-type maps.
- This derived result contradicts the diffusion coefficient curve presented in the referenced paper.
- A fractal diffusion coefficient is recalled as a solution for more general parameter values, referencing Markov partition-based approaches.
Key Insights:
- The random walk formula for diffusion coefficient is confirmed for Bernoulli-type maps.
- A discrepancy exists between the derived diffusion coefficient and the curve presented in Rajagopalan and Sabir's work.
- Fractal diffusion coefficients offer solutions for broader parameter ranges in piecewise linear maps.
Outlook:
- The model discussed by Rajagopalan and Sabir is deemed unsuitable for studying intermittent behavior.
- Further research may explore alternative models for analyzing intermittency in dynamical systems.
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