Lyapunov exponent {tseriesChaos}

Tools to evaluate the maximal Lyapunov exponent of a dynamic system

Description

Tools to evaluate the maximal Lyapunov exponent of a dynamic system from a univariate time series

Usage

lyap_k(series, m, d, t, k=1, ref, s, eps)
lyap(dsts, start, end)

Arguments

series

time series

m

embedding dimension

d

time delay

k

number of considered neighbours

eps

radius where to find nearest neighbours

s

iterations along which follow the neighbours of each point

ref

number of points to take into account

t

Theiler window

dsts

Should be the output of a call to lyap_k (see the example)

start

Starting time of the linear bite of dsts

end

Ending time of the linear bite of dsts

Details

The function lyap_k estimates the largest Lyapunov exponent of a given scalar time series using the algorithm of Kantz.

The function lyap computes the regression coefficients of a user specified segment of the sequence given as input.

Value

lyap_k gives the logarithm of the stretching factor in time.

lyap gives the regression coefficients of the specified input sequence.

Author(s)

Antonio, Fabio Di Narzo

References

Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)

M. T. Rosenstein, J. J. Collins, C. J. De Luca, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65, 117 (1993)

See Also

mutual, false.nearest for the choice of optimal embedding parameters. embedd to perform embedding.

Examples

output <-lyap_k(lorenz.ts, m=3, d=2, s=200, t=40, ref=1700, k=2, eps=4)
plot(output)
lyap(output, 0.73, 2.47)