NonLinModelling {fNonlinear}

Chaotic Time Series Modelling

Description

A collection and description of functions to simulate different types of chaotic time series maps.

Chaotic Time Series Maps:

tentSim	Simulates data from the Tent Map,
henonSim	simulates data from the Henon Map,
ikedaSim	simulates data from the Ikeda Map,
logisticSim	simulates data from the Logistic Map,
lorentzSim	simulates data from the Lorentz Map,
roesslerSim	simulates data from the Roessler Map.

Usage

tentSim(n = 1000, n.skip = 100, parms = c(a = 2), start = runif(1), 
    doplot = FALSE)
henonSim(n = 1000, n.skip = 100, parms = c(a = 1.4, b = 0.3), 
    start = runif(2), doplot = FALSE)
ikedaSim(n = 1000, n.skip = 100, parms = c(a = 0.4, b = 6.0, c = 0.9), 
    start = runif(2), doplot = FALSE)
logisticSim(n = 1000, n.skip = 100, parms = c(r = 4), start = runif(1), 
    doplot = FALSE)
lorentzSim(times = seq(0, 40, by = 0.01), parms = c(sigma = 16, r = 45.92, 
    b = 4), start = c(-14, -13, 47), doplot = TRUE, ...)
roesslerSim(times = seq(0, 100, by = 0.01), parms = c(a = 0.2, b = 0.2, c = 8.0),
    start = c(-1.894, -9.920, 0.0250), doplot = TRUE, ...) 

Arguments

doplot

a logical flag. Should a plot be displayed?

n, n.skip

[henonSim][ikedaSim][logisticSim] -
the number of chaotic time series points to be generated and the number of initial values to be skipped from the series.

parms

the named parameter vector characterizing the chaotic map.

start

the vector of start values to initiate the chaotic map.

times

[lorentzSim][roesslerSim] -
the sequence of time series points at which to generate the map.

...

arguments to be passed.

Value

[*Sim] -
All functions return invisible a vector of time series data.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

References

Brock, W.A., Dechert W.D., Sheinkman J.A. (1987); A Test of Independence Based on the Correlation Dimension, SSRI no. 8702, Department of Economics, University of Wisconsin, Madison.

Eckmann J.P., Oliffson Kamphorst S., Ruelle D. (1987), Recurrence plots of dynamical systems, Europhys. Letters 4, 973.

Hegger R., Kantz H., Schreiber T. (1999); Practical implementation of nonlinear time series methods: The TISEAN package, CHAOS 9, 413–435.

Kennel M.B., Brown R., Abarbanel H.D.I. (1992); Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A45, 3403.

Rosenstein M.T., Collins J.J., De Luca C.J. (1993); A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65, 117.

See Also

RandomInnovations.

Examples

## logisticSim -
   set.seed(4711)
   x = logisticSim(n = 100)  
   plot(x, main = "Logistic Map")