Transitivity?

Everything about quantification of recurrence plots and recurrence networks.
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UAFredens
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Affiliation (Univ., Inst., Dept.): Psychology, Aarhus University
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Transitivity?

Post by 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?
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Norbert
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Re: Transitivity?

Post by Norbert »

UAFredens wrote: Sun Apr 3, 2022 12:01 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.
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