tseriesChaos (version 0.1-13.1)

Lyapunov exponent: 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

Value

lyap_k gives the logarithm of the stretching factor in time. lyap gives the regression coefficients of the specified input sequence.

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.

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

# NOT RUN {
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)
# }