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Discriminating additive from dynamical noise for chaotic time series
Marek Strumik1, Wiesław M Macek, Stefano Redaelli
1Space Research Center, Polish Academy of Sciences, Bartycka 18 A, 00-716 Warsaw, Poland. maro@cbk.waw.pl
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Dynamical noise in chaotic systems like Hénon and Ikeda maps can mimic additive Cauchy pseudonoise. This finding enables a new method to distinguish between additive and dynamical noise in time series data.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Statistical physics
Background:
- Deterministic systems like Hénon and Ikeda maps can be corrupted by noise.
- Distinguishing between additive and dynamical noise is crucial for accurate analysis.
Purpose of the Study:
- To investigate the effect of dynamical noise on Hénon and Ikeda maps.
- To develop a method for discriminating between additive and dynamical noise.
- To estimate noise levels in chaotic time series.
Main Methods:
- Analysis of Hénon and Ikeda map dynamics under additive and dynamical noise.
- Characterization of noise distribution (Cauchy and Gaussian).
- Utilizing scaling properties of correlation entropy.
Main Results:
- Dynamical noise in specific variables can be effectively treated as additive Cauchy pseudonoise.
- Noise in the second variable remains Gaussian, independent of dynamical noise type.
- A method to discriminate between additive and dynamical noise was proposed and validated.
Conclusions:
- Dynamical noise in certain chaotic systems exhibits Cauchy-like distributions.
- The proposed method effectively distinguishes noise types and estimates noise levels.
- The approach is robust across a range of noise levels where one type predominates.