data.gen.Lorenz: Lorenz system
In synthesis: Generate Synthetic Data from Statistical Models

Description Usage Arguments Details Value Note References Examples

Generates a 3-dimensional time series using the Lorenz equations.

data.gen.Lorenz(
  sigma = 10,
  beta = 8/3,
  rho = 28,
  start = c(-13, -14, 47),
  time = seq(0, 50, length.out = 1000),
  s
)

`sigma`	The sigma parameter. Default: 10.
`beta`	The beta parameter. Default: 8/3.
`rho`	The rho parameter. Default: 28.
`start`	A 3-dimensional numeric vector indicating the starting point for the time series. Default: c(-13, -14, 47).
`time`	The temporal interval at which the system will be generated. Default: time=seq(0,50,by = 0.01).
`s`	The level of noise, default 0.

The Lorenz system is a system of ordinary differential equations defined as:

dx/dt = sigma*( y - x )

dy/dt = rho*x - y - xz

dz/dt = -beta*z + xy

The default selection for the system parameters (sigma=10, rho=28, beta=8/3) is known to produce a deterministic chaotic time series.

A list with four vectors named time, x, y and z containing the time, the x-components, the y-components and the z-components of the Lorenz system, respectively.

Some initial values may lead to an unstable system that will tend to infinity.

Constantino A. Garcia (2019). nonlinearTseries: Nonlinear Time Series Analysis. R package version 0.2.7. https://CRAN.R-project.org/package=nonlinearTseries

###Synthetic example - Lorenz
ts.l <- data.gen.Lorenz(sigma = 10, beta = 8/3, rho = 28, start = c(-13, -14, 47),
                        time = seq(0, by=0.05, length.out = 2000))

ts.plot(cbind(ts.l$x,ts.l$y,ts.l$z), col=c('black','red','blue'))