nonlinearTseries: ikedaMap – R documentation

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ikedaMap

Ikeda map

Generates a time series using the Ikeda map

ikedaMap(
  a = 0.85,
  b = 0.9,
  cc = 7.7,
  k = 0.4,
  start = runif(2),
  n.sample = 5000,
  n.transient = 500,
  do.plot = TRUE
)

`a`	The a parameter. Default: 0.85.
`b`	The b parameter. Default: 0.9.
`cc`	The c parameter. Default: 7.7.
`k`	The k parameter. Default: 0.4.
`start`	a 2-dimensional numeric vector 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 ikeda system is shown.

The Ikeda map is defined as follows:

z[n+1] = a + b*z[n]*exp(ik-ic/( 1+ |z_[n-1]|^2 ) )

The default selection for the a, b, c and k parameters is known to produce a deterministic chaotic time series.

a list with 2 vectors named x and y the x-components and the y-components of the Ikeda map, 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)

## Not run: 
ikeda.map=ikedaMap(n.sample = 1000, n.transient=10, do.plot=TRUE)

## End(Not run)

Nonlinear Time Series Analysis

v0.2.10

GPL-3

Authors

Constantino A. Garcia [aut, cre], Gunther Sawitzki [ctb]

Initial release

2020-6-10