Calculates local Lyapunov exponents for plotting.
Usage
lle(jac, model=1, nprod=c(5, 10, 20, 40, 80), skip, statevector=F,
lags=NA)
Arguments
jac
|
Jacobian matrix or a nnreg fit.
|
model
|
Model number of fit used to calculate Jacobians.
|
nprod
|
Vector of LLE products of Jacobians.
|
skip
|
Columns of Jacobian matrix to skip in calculating LLEs.
For example, skip the columns associated with forcing functions.
|
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.
|
lags
|
Lagged time values used in the Jacobian matrix.
|
Value
local
|
Matrix of LLEs with columns corresponding to the LLEs of the nprod values.
|
nprod
|
Vector of LLE products of Jacobians.
|
glb
|
Global Lyapunov exponent.
|
model
|
Model number used to calculate Jacobians.
|
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
make.lleExamples
make.lags(rossler.state[1:200,1],c(1,2,3)) -> data.r # create
# 3-d time delay vector model of the x variable of rossler system.
nnreg(data.r$x,data.r$y,5,5) -> fit # fit time series model using nnreg.
jac<- predict(fit, derivative=1)
lle(jac) -> rossler.lle # LLEs of Rossler data
summary(lle)
plot(rossler.lle) # plot LLEs
# here is an easier way
nlar( rossler[1:200], lags=1:3, method="nnreg", k1=5)-> ou
lle( out) -> rossler.lle