Lyapunov Exponent of Time Series Data

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The Lyapunov Exponent and how to compute it from time series data.

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Lyapunov Exponent of Time Series Data

  1. 1. Lyapunov Exponent of Time Series Data Abhranil Das
  2. 2. Slide 2 of 9
  3. 3. Lyapunov ExponentSlide 3 of 9
  4. 4. Lyapunov Exponent • Maximal Lyapunov exponent:Slide 4 of 9
  5. 5. Lyapunov ExponentSlide 5 of 9
  6. 6. Lyapunov exponent for Logistic mapSlide 6 of 9
  7. 7. Lyapunov exponent for Logistic mapSlide 7 of 9
  8. 8. Lyapunov exponent for Logistic mapSlide 8 of 9 slope ≈ 0.75, characteristic length ≈ 8
  9. 9. Lyapunov exponent for IBI time series • For this time series, <ln[d(k)]> turned out to be independent of both k and n, thus demonstrating that the IBI’s Ti are independent random variables. • Although note that this sequence is not strictly a 1D map.Slide 9 of 9

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