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Last data update: 2014.03.03

R: Lorenz system

lorenz

R Documentation

Lorenz system

Description

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

Usage

lorenz(sigma = 10, beta = 8/3, rho = 28, start = c(-13, -14, 47),
  time = seq(0, 50, by = 0.01), do.plot = TRUE)

Arguments

`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).
`do.plot`	Logical value. If TRUE (default value), a plot of the generated Lorenz system is shown.

Details

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.

Value

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.

Note

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

Author(s)

Constantino A. Garcia

References

Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)

Examples

## Not run: 
lor=lorenz(time=seq(0,30,by = 0.01))
# plotting the x-component
plot(lor$time,lor$x,type="l")

## End(Not run)