# lyapFDWolf: lyapFDWolf : computes Lyapunov spectrum with Wolf method In GPoM.FDLyapu: Lyapunov Exponents and Kaplan-Yorke Dimension

## Description

Computes all the Lyapunov exponents based on Gram-Schmidt procedure (Wolf et al. 1985). The Jacobian matrix is computed from the original model by semi-Formal Derivation.

## Usage

 ```1 2 3``` ```lyapFDWolf(outLyapFD = NULL, nVar, dMax, coeffF, intgrMthod = "rk4", tDeb = 0, dt, tFin, yDeb, Ddeb = NULL, nIterMin = 1, nIterStats = 50) ```

## Arguments

 `outLyapFD` List of output data that can be used as an input in order to extend the computation `nVar` Model dimension `dMax` Maximum degree of the polynomial formulation `coeffF` Model matrix. Each column correspond to one equation. Lines provide the coefficients for each polynomial term which order is defined with function `poLabs(nVar, dMax)` in package `GPoM`) `intgrMthod` Numerical integration method ('rk4' by default) `tDeb` Initial integration time (0 by default) `dt` Integration time step `tFin` Final integration time `yDeb` Model initial conditions `Ddeb` Jacobian initial conditions (optional). `nIterMin` Minimum number of iterations (nIterMin= 1 by default) `nIterStats` Number of iterations used in the statistics computation

## Value

List of output data

## References

A. Wolf, J. B. Swift, H. L. Swinney & J. A. Vastano, Determining Lyapunov exponents from a time series, Physica D, 285-317, 1985.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```data(Ebola) nVar = dim(Ebola\$KL) pMax = dim(Ebola\$KL) dMax = p2dMax(nVar, pMax) outLyapFD <- NULL outLyapFD\$Wolf <- lyapFDWolf(outLyapFD\$Wolf, nVar= nVar, dMax = dMax, coeffF = Ebola\$KL, tDeb = 0, dt = 0.01, tFin = 2, yDeb = Ebola\$yDeb) ```

GPoM.FDLyapu documentation built on Aug. 29, 2019, 5:05 p.m.