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Related Experiment Videos

Lyapunov spectrum from time series using moving boxes.

N N Oiwa1, N Fiedler-Ferrara

  • 1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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We developed a fast algorithm to estimate the Lyapunov spectrum from time series data. This method is robust, requiring fewer parameters and performing well even with noisy or imprecise plasma data.

Area of Science:

  • Plasma physics
  • Nonlinear dynamics
  • Time series analysis

Background:

  • Estimating the Lyapunov spectrum is crucial for understanding the dynamics of complex systems.
  • Traditional methods can be computationally intensive and sensitive to data quality.
  • Plasma edge turbulence exhibits complex, chaotic behavior.

Purpose of the Study:

  • To present a novel, rapid algorithm for calculating the full Lyapunov spectrum from time series data.
  • To assess the algorithm's robustness against variations in data precision, sampling, and noise.
  • To apply the algorithm to analyze electron density fluctuations in tokamak plasma.

Main Methods:

  • A new time-series-based algorithm for Lyapunov spectrum estimation.
  • Testing across diverse numerical precisions, sampling frequencies, and durations.

Related Experiment Videos

  • Inclusion of noise in data to evaluate algorithm resilience.
  • Application to experimental data from the edge of tokamak TBR-1.

    • Main Results:

    • The algorithm achieves Lyapunov spectrum estimation within seconds.
    • Robust performance demonstrated across varied data conditions (precision, sampling, noise).
    • Successful application to electron density broadband fluctuations in tokamak plasma.

    Conclusions:

    • The presented algorithm offers a fast and reliable method for Lyapunov spectrum estimation.
    • Its robustness makes it suitable for analyzing complex experimental data, such as tokamak edge plasmas.
    • This advancement facilitates deeper insights into plasma dynamics and chaotic systems.