Then calculate a symmetry
Q(k) = ( RR(k) + RR(-k) ) / 2
and an asymmetry measure
q(k) = ( RR(k) - RR(-k) ) / 2.
The graph of both measures over the time lag k shows whether both systems are coupled/synchronised and which system leads the other. These measures can also be calculated from the other RQA measures.
![Image](http://www.recurrence-plot.tk/img/fig_diagonal_RQA.gif)
This plot shows these proposed symmetry and asymmetry measures derived from RR(k) for two coupled Roessler oscillators. The maxima of the (A) symmetry measure at lag 0.3 reveals the lag-coupling, and (B) the negative value of the asymmetry measure athe the same lag reveals that the second system leads the first one.
I got this idea by reading
Quian Quiroga et al, Event synchronization: A simple and fast method to measure synchronicity and time delay patterns, PRE 66, 041904, 2002
Perhaps someone find it useful.
![Cool 8)](./images/smilies/icon_cool.gif)
Regards,
Norbert