Description Usage Arguments Details Value Note Author(s) References See Also Examples
Generates a 3-dimensional time series using the Lorenz equations.
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start |
A 3-dimensional numeric vector indicating the starting point for the time series. Default: c(-13, -14, 47). |
sigma |
The sigma parameter. Default: 10. |
rho |
The rho parameter. Default: 28. |
beta |
The beta parameter. Default: 8/3. |
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. |
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
Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)
henon, logisticMap, rossler,
ikedaMap, cliffordMap, sinaiMap,
gaussMap
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