henon: Henon map

In nonlinearTseries: Nonlinear Time Series Analysis

Description

Generates a 2-dimensional time series using the Henon map.

Usage

henon(start = runif(min = -0.5, max = 0.5, n = 2), a = 1.4, b = 0.3,
  n.sample = 5000, n.transient = 500, do.plot = TRUE)

Arguments

start	A 2-dimensional vector indicating the starting values for the x and y Henon coordinates. If the starting point is not specified, it is generated randomly.
a	The a parameter. Default: 1.4.
b	The b parameter. Default: 0.3.
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 Henon system is shown.

Details

The Henon map is defined as follows:

x[n] = 1 - a*x[n - 1]^2 + y[n - 1]

y[n] = b*x[n - 1].

The default selection for both a and b parameters (a=1.4 and b=0.3) is known to produce a deterministic chaotic time series.

Value

A list with two vectors named x and y containing the x-components and the y-components of the Henon 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

logisticMap, lorenz, rossler, ikedaMap, cliffordMap, sinaiMap, gaussMap

Examples

## Not run: 
henon.map=henon(n.sample = 1000, n.transient=10,do.plot=TRUE,
               start=c(-0.006423277,-0.473545134))
# accessing the x coordinate and plotting it
plot(ts(henon.map$x))

## End(Not run)

Example output

Loading required package: Matrix
Loading required package: rgl
Loading required package: tseries
Loading required package: TSA
Loading required package: leaps
Loading required package: locfit
locfit 1.5-9.1 	 2013-03-22
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.

Attaching package: 'TSA'

The following objects are masked from 'package:stats':

    acf, arima

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

    tar

Loading required package: Rcpp

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 

nonlinearTseries documentation built on May 2, 2019, 5:47 p.m.