Generating surrogates from recurrences

M Thiel, M C Romano, J Kurths, M Rolfs, R Kliegl

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.
Original languageEnglish
Pages (from-to)545-557
Number of pages13
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Issue number1865
Early online date13 Aug 2007
Publication statusPublished - 28 Feb 2008


  • recurrence plots
  • surrogate data
  • hypothesis test
  • phase synchronization
  • covert attention
  • eye-movements
  • systems
  • dynamics
  • plots


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