Lyapunov: Tools to evaluate the maximal Lyapunov exponent of a dynamic...

In tseriesChaos: Analysis of Nonlinear Time Series

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)

Example output

Loading required package: deSolve
Finding nearests
Keeping  1700  reference points
Following points
(Intercept)      lambda 
  0.1185032   0.7123131 

tseriesChaos documentation built on May 2, 2019, 6:38 a.m.