nonlinearTseries: gaussMap – R documentation

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gaussMap

Gauss map

Generates a 1-dimensional time series using the Gauss map

gaussMap(
  a = 4.9,
  b = -0.58,
  start = runif(1, min = -0.5, max = 0.5),
  n.sample = 5000,
  n.transient = 500,
  do.plot = TRUE
)

`a`	The a parameter. Default: 4.9
`b`	The b parameter. Default: -0.58
`start`	A numeric value indicating the starting value for the time series. If the starting point is not specified, it is generated randomly.
`n.sample`	Length of the generated time series. Default: 5000 samples.
`n.transient`	Number of transient samples that will be discarded. Default: 500 samples.
`do.plot`	Logical value. If TRUE (default value), a plot of the generated Gauss system is shown.

The Gauss map is defined as follows:

x[n+1] = exp(-a*(x[n])^2) + b

The default selection for both a and b parameters is known to produce a deterministic chaotic time series.

A vector containing the values of the time series that has been generated.

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

Constantino A. Garcia

Chaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004.