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Asymptotic behavior of the time-dependent divergence exponent
Leonardo Ricci1, Alessio Perinelli1, Matteo Franchi1
1Department of Physics, University of Trento, 38123 Trento, Italy.
Physical Review. E
|May 20, 2020
Summary
This study introduces a divergence rate method to analyze time series. It can distinguish chaotic systems from noise and estimate correlation dimensions, offering a new tool for dynamical system analysis.
Area of Science:
- Dynamical Systems and Chaos Theory
- Nonlinear Time Series Analysis
Background:
- The maximum Lyapunov exponent quantifies chaos in dynamical systems.
- Time series analysis often requires distinguishing deterministic chaos from stochastic processes.
- Previous methods for estimating Lyapunov exponents have limitations in practical applications.
Purpose of the Study:
- To introduce and evaluate a divergence rate method for determining the maximum Lyapunov exponent from time series data.
- To develop a novel approach for differentiating between stochastic and deterministic (chaotic) time series.
- To provide a precise estimation of the correlation dimension for chaotic systems.
Main Methods:
- Evaluation of the time-dependent divergence exponent.
- Analysis of the asymptotic "plateau" behavior of the divergence exponent.
- Comparison of time series generated by white noise and finite-dimensional chaotic systems.
Main Results:
- The divergence rate method exhibits distinct "plateau" behaviors for chaotic systems versus white noise.
- The method successfully distinguishes between purely stochastic and deterministic sources.
- Accurate estimation of the correlation dimension for chaotic systems was achieved.
- Sensitivity to correlated noise sources was demonstrated.
Conclusions:
- The divergence rate method offers a robust tool for characterizing dynamical systems from time series.
- This approach provides a reliable means to identify chaos and quantify its properties.
- The method's sensitivity to noise characteristics enhances its utility in complex data analysis.
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