lorenz {nonlinearTseries}

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 = deprecated()
)

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, a plot of the generated Lorenz system is shown. Before version 0.2.11, default value was TRUE; versions 0.2.11 and later use FALSE as default.

Details

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

\dot{x} = \sigma(y-x)

\dot{y} = \rho x-y-xz

\dot{z} = -\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)

See Also

henon, logisticMap, rossler, ikedaMap, cliffordMap, sinaiMap, gaussMap

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)