ikedaMap: Ikeda map

In nonlinearTseries: Nonlinear Time Series Analysis

Ikeda map

Description

Generates a time series using the Ikeda map

Usage

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

Arguments

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

Details

The Ikeda map is defined as follows:

z_{n+1} = a + b \cdot z_n \cdot exp( ik-\frac{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)

nonlinearTseries documentation built on Sept. 23, 2024, 5:10 p.m.