# Ikeda map

### Description

Generates a time series using the Ikeda map

### Usage

1 2 3 |

### Arguments

`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. |

`a` |
The |

`b` |
The |

`c` |
The |

`k` |
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 ikeda system is shown. |

### Details

The Ikeda map is defined as follows:

*z[n+1] = a + b*z[n]*exp(ik-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

1 2 3 4 |