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.

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,
radius=1.2,lmin=2,do.plot=FALSE,distanceToBorder=2)
plot(rqa.analysis)
## End(Not run)