gaussMap {nonlinearTseries}

Gauss map

Description

Generates a 1-dimensional time series using the Gauss map

Usage

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

Arguments

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

Details

The Gauss map is defined as follows:

x_{n+1}= exp(-a \cdot (x_n)^2) + b

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

Value

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

Note

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

Author(s)

Constantino A. Garcia

References

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

See Also

henon, logisticMap, lorenz, rossler, ikedaMap, cliffordMap, sinaiMap