How to find out which system leads the other by using CRPs

Everything about quantification of recurrence plots and recurrence networks.
Post Reply
User avatar
Norbert
Expert
Posts: 194
Joined: Wed Jan 4, 2006 11:03
Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

How to find out which system leads the other by using CRPs

Post by Norbert »

In order to find out which system drives the other, from the CRP you could compute a RQA measure defined diagonal-wise (i.e. not for the entire RP but only for the kth diagonal parallel to the LOI), e.g. RR(k). The measure RR(k) or RR(-k) means the recurrence density in the diagonal above or below the LOI (with distance k from the LOI). The variable k hat the meaning of a time lag.

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
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. 8)

Regards,
Norbert
Last edited by Norbert on Sun May 1, 2011 21:23, edited 1 time in total.
User avatar
geo
Junior
Posts: 4
Joined: Thu Mar 23, 2006 15:15
Location: Ghent, Belgium

Post by geo »

:D Just what my doctor ordened :lol: :lol:

Thanks very much.

Georges
Dr. G. Otte
Neuropsychiatry+Neurophysiology
PC dr Guislain Neurolab
Ferrerlaan 66A
9000 Gent
Belgium
09 216 33 11
User avatar
sultornsanee
Senior
Posts: 29
Joined: Tue Oct 12, 2010 21:05
Affiliation (Univ., Inst., Dept.): Northeastern University
Location: Boston, Massachusetts, USA
Research field: Pattern Recognition Analysis
Location: Network/Nano Science and Engineering Laboratory, Northeastern University, Boston, USA

Re: How to find out which system leads the other by using CR

Post by sultornsanee »

I am not clear about your answer here. Also an image is already gone. Could you explain to me again? :D ... Please
User avatar
Norbert
Expert
Posts: 194
Joined: Wed Jan 4, 2006 11:03
Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

Re: How to find out which system leads the other by using CR

Post by Norbert »

You can find these information in our Physics Reports paper.
N. Marwan, M. C. Romano, M. Thiel, J. Kurths: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5-6), 237-329, 2007

Best
Norbert
Post Reply