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Large deviations in chaotic systems: Exact results and dynamical phase transition.
1Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel.
Physical Review. E
|November 18, 2022
Summary
This study analyzes large deviations in chaotic dynamics, finding exponential decay in finite series. Researchers derived exact rate functions for several chaotic maps, revealing potential dynamical phase transitions.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Chaos theory
Background:
- Chaotic systems exhibit sensitive dependence on initial conditions.
- Large deviations in chaotic dynamics can lead to significant consequences.
- Understanding the statistical properties of finite-length chaotic sequences is crucial.
Purpose of the Study:
- To investigate large deviations in finite-length series generated by chaotic maps.
- To derive and analyze the associated large-deviation (rate) functions.
- To explore potential dynamical phase transitions in chaotic systems.
Main Methods:
- Analytical derivation of rate functions for specific chaotic maps (doubling, tent, logistic).
- Numerical computation of rate functions for the cat map.
- Development of a numerical tool for simulating atypical realizations in non-invertible maps.
Main Results:
- Distributions of large deviations generally show exponential decay with series length N.
- Exact analytical rate functions were obtained for the doubling, tent, and logistic maps.
- Numerical analysis of the cat map revealed a singularity interpreted as a second-order dynamical phase transition.
- An efficient numerical simulation tool was developed for non-invertible chaotic maps.
Conclusions:
- Large deviations in chaotic dynamics can be characterized by rate functions, often exhibiting exponential decay.
- The study provides exact solutions for several key chaotic maps and uncovers evidence of phase transitions.
- The developed numerical tool facilitates the study of atypical behaviors in non-invertible chaotic systems.
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