Scaling behaviour for recurrence-based measures at the edge of chaos

Ozgur Afsar, Deniz Eroglu, Norbert Marwan, Jurgen Kurths

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The study of phase transitions with critical exponents has helped to understand fundamental physical mechanisms. Dynamical systems which go to chaos via period doublings show an equivalent behavior during transitions between different dynamical regimes that can be expressed by critical exponents, known as the Huberman-Rudnick scaling law. This universal law is well studied, e.g., with respect to the Lyapunov exponents. Recurrence plots and related recurrence quantification analysis are popular tools to investigate the regime transitions in dynamical systems. However, the measures are mostly heuristically defined and lack clear theoretical justification. In this letter we link a selection of these heuristical measures with theory by numerically studying their scaling behavior when approaching a phase transition point. We find a promising similarity between the critical exponents to those of the Huberman-Rudnick scaling law, suggesting that the considered measures are able to indicate dynamical phase transition even from the theoretical point of view.
Original languageEnglish
Article number10005
Number of pages7
JournalEurophysics Letters
Issue number1
Publication statusPublished - 19 Oct 2015

Bibliographical note

OA acknowledges support by TUBITAK (Turkish Agency) under the 2219 Program. DE and NM would like to acknowledge support by the Leibniz Association (WGL) under Grant No. SAW-2013-IZW-2. NM acknowledges support by DFG Research Training Group GRK 2043/1.


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