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Estimates the largest Lyapunov exponent from the average logarithmic divergence of initially nearby trajectories in a delay-embedded phase space (Rosenstein et al. 1993). A positive exponent indicates sensitive dependence on initial conditions (chaos / local instability).

Usage

maxLyapunovExponent(
  x,
  delay = NULL,
  dim = NULL,
  sampling_rate = 1,
  mean_period = NULL,
  max_steps = NULL,
  fit_range = NULL
)

Arguments

x

Numeric time series.

delay, dim

Embedding delay and dimension; NULL estimates them via timeDelayEmbed().

sampling_rate

Sampling rate in Hz (scales the exponent to per-second).

mean_period

Theiler window in samples excluding temporally-close neighbours; NULL estimates it from the mean signal period.

max_steps

Number of forward steps to track divergence; NULL uses a default derived from the series length.

fit_range

Integer vector c(from, to) (in steps) of the divergence curve to fit the slope; NULL uses an early near-linear window.

Value

A lyapunov_exponent object with lambda (per second), the divergence curve, fit_range, delay and dim.

References

Rosenstein MT, Collins JJ, De Luca CJ (1993). Physica D 65:117-134.