A point i,j in this plot is set if
with being the set of M nearest
neighbours of
; i.e. if
is one of the
nearest neighbours of
and if it lies within a
sphere of radius r around the current reference point.
Since the coordinates i and j represent points on a time axis, recurrence plots give information about the temporal correlation of phase space points.
From the occurrence of lines parallel to the diagonal in the recurrence plot it can be seen how fast neighboured trajectories diverge in phase space. Therefore, the average length of these lines is a measure of the reciprocal of the largest positive Lyapunov exponent.
Recurrence plots help revealing phase transitions and instationarities.
Visible rectangular block structures with a higher
density of points in the recurrence plot indicate phase transitions
within the signal. If the texture of the pattern within such a block
is homogeneous, stationarity can be assumed for the given signal
within the corresponding period of time.
Parameters are:
Note that y is a 2D plot.