# Gauss map

### Description

Generates a 1-dimensional time series using the Gauss map

### Usage

1 2 3 |

### Arguments

`start` |
A numeric value indicating the starting value for the time series. If the starting point is not specified, it is generated randomly. |

`a` |
The |

`b` |
The |

`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 Gauss system is shown. |

### Details

The Gauss map is defined as follows:

*x[n+1] = exp(-a*(x[n])^2) + b*

The default selection for both *a* and *b*
parameters is known to produce a deterministic chaotic
time series.

### Value

A vector containing the values of the time series that has been generated.

### Note

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

### Author(s)

Constantino A. Garcia

### References

Chaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004.

### See Also

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