# cliffordMap: Clifford map In nonlinearTseries: Nonlinear Time Series Analysis

## Description

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

## Usage

 ```1 2``` ```cliffordMap(a = -1.4, b = 1.6, cc = 1, d = 0.7, start = runif(2), n.sample = 5000, n.transient = 500, do.plot = TRUE) ```

## Arguments

 `a` The a parameter. Default: -1.4 `b` The b parameter. Default: 1.6 `cc` The c parameter. Default: 1.0 `d` The d parameter. Default: 0.7 `start` a 2-dimensional vector indicating the starting values for the x and y Clifford coordinates. 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 (default value), a plot of the generated Clifford system is shown.

## Details

The Clifford map is defined as follows:

x[n+1] = sin(a*y[n]) + c*cos(a*x[n])

y[n+1] = sin(b*x[n] + d*cos(b*y[n])

The default selection for the a b c and d parameters 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 Clifford map, respectively.

## Note

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

## Author(s)

Constantino A. Garcia

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

## Examples

 ```1 2 3 4 5``` ```## Not run: clifford.map=cliffordMap(n.sample = 1000, n.transient=10,do.plot=TRUE) # accessing the x coordinate and plotting it plot(ts(clifford.map\$x)) ## End(Not run) ```

### Example output  ```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