ikedaMap: Ikeda map
In nonlinearTseries: Nonlinear Time Series Analysis

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Generates a time series using the Ikeda map

1 2	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)

henon, logisticMap, lorenz, rossler, cliffordMap, sinaiMap, gaussMap

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

## End(Not run)

Attaching package: 'nonlinearTseries'

The following object is masked from 'package:grDevices':

    contourLines

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found