henon: Henon map In nonlinearTseries: Nonlinear Time Series Analysis

Description

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

Usage

 ```1 2``` ```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)

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

Examples

 ```1 2 3 4 5 6 7``` ```## 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
locfit 1.5-9.1 	 2013-03-22
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

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