NLDSD_LorenzAttractor: Attractor of Lorenz
In faustogc/streamChaos: Analysis of Non Linear Data Streams

Description Usage Arguments Details Value Author(s) References See Also Examples

A data stream generator based on the three-dimensional Lorenz Attractor.

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NLDSD_LorenzAttractor(N, start.x=c(5, 5, 5), parms=c(10, 28, 8/3),
                      dt=0.1, warming.up.num=1000, range=NULL,
                      noise.type="None", noise.parms=list())

`N`	Determines the data stream length.
`start.x`	Determines the initial condition.
`parms`	The set of parameters σ, ρ, and β for the Lorenz' three-dimensional equation.
`dt`
`warming.up.num`	Number of observations for warming up the attractor.
`range`
`noise.type`	Type of the noise ("None", "Uniform", "Normal")
`noise.parms`	A list for generating the noise.

NLDSD_LorenzAttractor creates a data stream based on the three-dimensional Lorenz Attractor:

x_{t+1} = σ (y - x_t), y_{t+1} = x_t (ρ - z_t) - y_t, z_{t+1} = x_t y_t - β z_t,

in which the parameters σ, ρ, and β change the data behavior. Traditionally, they are set to 10, 28, and 8/3 respectively, producing a chaotic data. Other values may be used, as shown in Wikipedia.

In this code, only the variable x_t is returned.

Returns a NLDSD_LorenzAttractor object (subclass of NLDSD) which is a list of the defined params.

Fausto Guzzo da Costa

https://en.wikipedia.org/wiki/Lorenz_system

NLDSD

# create a data stream with 10,000 observations based on a Logistic Map
# and plot it
stream1 <- NLDSD_LorenzAttractor(N=10000)
plot(stream1)


# create a data stream with 10,000 observations based on a Logistic Map
# with noise produced by a Normal distribution
# with mean=0 and std=0.1
# and plot it
stream2 <- NLDSD_LorenzAttractor(N=10000, noise.type="Normal",
                                 noise.parms=list(mean=0, sd=0.1))
plot(stream2)