Last data update: 2014.03.03

R: Recurrence Quantification Analysis (RQA)
 rqa R Documentation

## Recurrence Quantification Analysis (RQA)

### Description

The Recurrence Quantification Analysis (RQA) is an advanced technique for the nonlinear analysis that allows to quantify the number and duration of the recurrences in the phase space.

### Usage

```rqa(takens = NULL, time.series = NULL, embedding.dim = 2, time.lag = 1,
radius, lmin = 2, vmin = 2, distanceToBorder = 2, save.RM = TRUE,
do.plot = FALSE, ...)
```

### Arguments

 `takens` Instead of specifying the time.series, the embedding.dim and the time.lag, the user may specify directly the Takens' vectors. `time.series` The original time series from which the phase-space reconstruction is performed. `embedding.dim` Integer denoting the dimension in which we shall embed the time.series. `time.lag` Integer denoting the number of time steps that will be use to construct the Takens' vectors. `radius` Maximum distance between two phase-space points to be considered a recurrence. `lmin` Minimal length of a diagonal line to be considered in the RQA. Default lmin = 2. `vmin` Minimal length of a vertical line to be considered in the RQA. Default vmin = 2. `distanceToBorder` In order to avoid border effects, the distanceToBorder points near the border of the recurrence matrix are ignored when computing the RQA parameters. Default, distanceToBorder = 2. `save.RM` Logical value. If TRUE, the recurrence matrix is stored as a sparse matrix. Note that computing the recurrences in matrix form can be computationally expensive. `do.plot` Logical. If TRUE, the recurrence plot is shown. However, plotting the recurrence matrix is computationally expensive. Use with caution. `...` Additional plotting parameters.

### Value

A rqa object that consist of a list with the most important RQA parameters:

• recurrence.matrix: A sparse symmetric matrix containing the recurrences of the phase space.

• REC: Recurrence. Percentage of recurrence points in a Recurrence Plot.

• DET: Determinism. Percentage of recurrence points that form diagonal lines.

• LAM: Percentage of recurrent points that form vertical lines.

• RATIO: Ratio between DET and RR.

• Lmax: Length of the longest diagonal line.

• Lmean: Mean length of the diagonal lines. The main diagonal is not taken into account.

• DIV: Inverse of Lmax.

• Vmax: Longest vertical line.

• Vmean: Average length of the vertical lines. This parameter is also referred to as the Trapping time.

• ENTR: Shannon entropy of the diagonal line lengths distribution

• TREND: Trend of the number of recurrent points depending on the distance to the main diagonal

• diagonalHistogram: Histogram of the length of the diagonals.

• recurrenceRate: Number of recurrent points depending on the distance to the main diagonal.

### Author(s)

Constantino A. Garcia and Gunther Sawitzki

### References

Zbilut, J. P. and C. L. Webber. Recurrence quantification analysis. Wiley Encyclopedia of Biomedical Engineering (2006).

### Examples

```## Not run:
rossler.ts =  rossler(time=seq(0, 10, by = 0.01),do.plot=FALSE)\$x
rqa.analysis=rqa(time.series = rossler.ts, embedding.dim=2, time.lag=1,
```