DkyCalc: DkyCalc : computes the Kaplan-Yorke dimension

In GPoM.FDLyapu: Lyapunov Exponents and Kaplan-Yorke Dimension

Description

Computes the Kaplan-Yorke dimension from the Lyapunov exponents (Kaplan and Yorke 1979).

Usage

DkyCalc(methodName, nVar, lyapExp)

Arguments

methodName	The method that was used to compute the lyapunov exponents
nVar	The model dimension (which corresponds to the number of exponents)
lyapExp	Time series of the local Lyapunov exponents spectrum (one column for each exponent)

References

Kaplan, J. & Yorke, J., Chaotic behavior of multidimensional difference equations. In: Peitgen H. O. and Walther H. O., "Functional Differential Equations and the Approximation of Fixed Points", Lecture Notes in Mathematics. 730. Berlin: Springer. p. 204-227, 1979.

Examples

#' Load the global model (here for Ebola Virus Diesease)
data(Ebola)
nVar = dim(Ebola$KL)[2]
pMax = dim(Ebola$KL)[1]
dMax = p2dMax(nVar, pMax)
#' Compute the time series of Lyapunov exponents
outLyapFD <- NULL
outLyapFD$Wolf <- lyapFDWolf(outLyapFD$Wolf, nVar= nVar, dMax = dMax,
                             coeffF = Ebola$KL,
                             tDeb = 0, dt = 0.01, tFin = 2,
                             yDeb = Ebola$yDeb)
#' estimate the Kaplan-Yorke dimension
DkyCalc(methodName = "Wolf", nVar= 3, lyapExp = outLyapFD$Wolf$lyapExpLoc)

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