ikedaMap: Ikeda map

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

View source: R/nonLinearSystems.R

Description

Generates a time series using the Ikeda map

Usage

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  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

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

## End(Not run)

nonlinearAnalysis documentation built on May 21, 2017, 3:43 a.m.

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