Lyapunov exponent {tseriesChaos} | R Documentation |
Tools to evaluate the maximal Lyapunov exponent of a dynamic system from a univariate time series
lyap_k(series, m, d, t, k=1, ref, s, eps) lyap(dsts, start, end)
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 |
start |
Starting time of the linear bite of |
end |
Ending time of the linear bite of |
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.
lyap_k
gives the logarithm of the stretching factor in time.
lyap
gives the regression coefficients of the specified input sequence.
Antonio, Fabio Di Narzo
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)
mutual
, false.nearest
for the choice of optimal embedding parameters.
embedd
to perform embedding.
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)