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.lle

Examples

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


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