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

1. Lyapunov Exponent of Time
Series Data
Abhranil Das

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3. Lyapunov Exponent
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4. Lyapunov Exponent
• Maximal Lyapunov exponent:
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5. Lyapunov Exponent
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6. Lyapunov exponent for Logistic map
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7. Lyapunov exponent for Logistic map
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8. Lyapunov exponent for Logistic map
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slope ≈ 0.75, characteristic length ≈ 8

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.
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