ikedaMap: Ikeda map

In nonlinearAnalysis: R package for nonlinear time series analysis

Description

Generates a time series using the Ikeda map

Usage

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

Arguments

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.
a	The a parameter. Default: 0.85.
b	The b parameter. Default: 0.9.
c	The c parameter. Default: 7.7.
k	The k parameter. Default: 0.4.
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.

Details

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.

Value

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

Note

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

Author(s)

Constantino A. Garcia

References

Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)

See Also

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

Examples

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

## End(Not run)

nonlinearAnalysis documentation built on May 2, 2019, 6:11 p.m.