Transitivity?

[UAFredens]

Referring to Reference Manual Version 5.22, Release 32, are there any scientific papers defing or discussing "local recurrence rate" and RQA measure #13, Transitivity?

[Norbert]

Referring to Reference Manual Version 5.22, Release 32, are there any scientific papers defing or discussing "local recurrence rate" and RQA measure #13, Transitivity?

There are not so many on the local RR (although I have included it in my lectures on recurrence analysis). The first one (that I know) is this one:

• H. Voss, J. Kurths, U. Schwarz: Reconstruction of grand minima of solar activity from radiocarbon data, Journal of Geophysical Research, 101, 15637–15643p. (1996). DOI:10.1029/96JA00542

It is often used to estimate the probability of a certain state, then applied in coupling analysis, e.g.:

• Y. Zou, M. C. Romano, M. Thiel, N. Marwan, J. Kurths: Inferring Indirect Coupling by Means of Recurrences, International Journal of Bifurcation and Chaos, 21(4), 1099–1111p. (2011). DOI:10.1142/S0218127411029033
• A. M. T. Ramos, A. Builes-Jaramillo, G. Poveda, B. Goswami, E. E. N. Macau, J. Kurths, N. Marwan: Recurrence measure of conditional dependence and applications, Physical Review E, 95, 052206p. (2017). DOI:10.1103/PhysRevE.95.052206

Network transitivity can be found in many studies, the first one is (although there it was called “clustering”):

• N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, J. Kurths: Complex network approach for recurrence analysis of time series, Physics Letters A, 373(46), 4246–4254p. (2009). DOI:10.1016/j.physleta.2009.09.042

Interesting interpretation in terms of a dimension:

• R. V. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths: The Geometry of Chaotic Dynamics – A Complex Network Perspective, European Physical
  Journal B, 84, 653–672p. (2011). DOI:10.1140/epjb/e2011-10899-1

I hope this helps.