lyapFDGrond: lyapFDGrond : Computes the Lyapunov spectrum (with compelled...

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

Description

Computes all the Lyapunov exponents based on Gram-Schmidt procedure with zero-Lyapunov exponent compelled to the flow direction (Grond et al. 1985). The Jacobian matrix is computed from the original model by semi-Formal Derivation.

Usage

lyapFDGrond(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

F. Grond, H. H. Diebner, S. Sahle, A. Mathias, S. Fischer, O. E. Rossler, A robust, locally interpretable algorithm for Lyapunov exponents, Chaos, Solitons \& Fractals, 16, 841-852 (2003).

F. Grond \& H. H. Diebner: Local Lyapunov exponents for dissipative continuous systems. Chaos, Solitons \& Fractals, 23, 1809-1817 (2005).

Examples

data(Ebola)
nVar = dim(Ebola$KL)[2]
pMax = dim(Ebola$KL)[1]
dMax = p2dMax(nVar, pMax)
outLyapFD <- NULL
outLyapFD$Grond <- lyapFDGrond(outLyapFD$Grond, 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.