Calculates global and local Lyapunov exponents
Usage
make.lle(jac, nprod, statevector=F, verbose=T)
Arguments
jac
|
Jacobian matrix, the value of the partial derivatives evaluated at each time.
|
nprod
|
Number of products of Jacobians multiplied together to calculate LLE.
If nprod is -1, the global LE is calculated.
|
statevector
|
If false, a time-delay reconstruction model is assumed and a Jacobian matrix
n by d is expected, where n is the length of the time series and d is the
dimension of the state space.
If true, a state space vector model is assumed and a Jacobian matrix n by d^2
is expected.
|
verbose
|
Statements are printed to the screen.
|
Description
Value
Two column matrix whose columns correspond the the calculation using a
singular value decomposition of the Jacobian matrix products or the
magnitude of the (1,1) entry of the Jacobian matrix products. The rows of
the matrix are the values of the LLEs at the time or the global LE.References
S. Ellner, D.W. Nychka, and A.R. Gallant. 1992. LENNS, a
program to estimate the dominant Lyapunov exponent of
noisy nonlinear systems from time series data. Institute
of Statistics Mimeo Series #2235, Statistics Department,
North Carolina State University, Raleigh, NC 27695-8203.See Also
lleExamples
make.lags(rossler.state[1:200,1],c(1,2,3)) -> data # create
# 3-d time delay vector model of the x variable of rossler system.
nnreg(data$x,data$y,5,5) -> fit # fit time series model using nnreg.
predict(fit,fit$x,derivative=1) -> jac # calculate Jacobian matrix
make.lle(jac,-1) -> rossler.le # LE of Rossler data