@article{ScheffczykEngbertKurthsetal.1995,
  author    = {Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold},
  title     = {Nonlinear Phenomena in Polyrhythmic Hand Movements},
  isbn      = {981-02-2689-6},
  year      = {1995},
  abstract  = {In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.},
  language  = {en}
}
@article{ScheffczykKrampeEngbertetal.1997,
  author    = {Scheffczyk, Christian and Krampe, Ralf-Thomas and Engbert, Ralf and Rosenblum, Michael and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Tempo-induced transitions in polyrhythmic hand movements},
  year      = {1997},
  abstract  = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.},
  language  = {en}
}
@article{SchiekScheffczykEngbertetal.1997,
  author    = {Schiek, Michael and Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold and Drepper, Friedhelm R.},
  title     = {Symbolic dynamics of physiological synchronisation : examples from bimanual movements and cardiorespiratory interaction},
  year      = {1997},
  abstract  = {Key words: Nonlinear time series analysis, symbolic dynamics, phase transitions, physiological data, biological synchronization, production of polyrhythms, cardiorespiratory interaction, variation of control parameter},
  language  = {en}
}
@article{ZaikinRosenblumScheffczyketal.1997,
  author    = {Zaikin, Alexei A. and Rosenblum, Michael and Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen},
  title     = {Modeling qualitative changes in bimanual movements},
  year      = {1997},
  language  = {en}
}
@article{KrampeEngbertKliegletal.2000,
  author    = {Krampe, Ralf-Thomas and Engbert, Ralf and Kliegl, Reinhold and Kurths, J{\"u}rgen},
  title     = {Koordination und Synchronisation der H{\"a}nde beim rhythmischen Timing},
  year      = {2000},
  language  = {de}
}
@article{RomanoThielKurthsetal.2006,
  author    = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Rolfs, Martin and Engbert, Ralf and Kliegl, Reinhold},
  title     = {Synchronization Analysis and Recurrence in Complex Systems},
  isbn      = {978-3-527-40623-4},
  year      = {2006},
  language  = {en}
}
@article{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Twin surrogates to test for complex synchronisation},
  doi       = {10.1209/epl/i2006-10147-0},
  year      = {2006},
  abstract  = {We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems},
  language  = {en}
}
@book{OsipovKurthsZhou2007,
  author    = {Osipov, Grigory V. and Kurths, J{\"u}rgen and Zhou, Changsong},
  title     = {Synchronisation in Oscillatory Networks},
  publisher = {Springer-Verlag},
  address   = {Berlin},
  isbn      = {978-3-540-71268-8},
  pages     = {368 S.},
  year      = {2007},
  language  = {en}
}
@article{ThielRomanoKurthsetal.2008,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Generating surrogates from recurrences},
  issn      = {1364-503X},
  year      = {2008},
  abstract  = {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.},
  language  = {en}
}
@article{MoshelZivotofskyLiangetal.2008,
  author    = {Moshel, Shay and Zivotofsky, Ari Z. and Liang, Jin-Rong and Engbert, Ralf and Kurths, J{\"u}rgen and Kliegl, Reinhold and Havlin, Shlomo},
  title     = {Persistence and phase synchronization properties of fixational eye movement},
  issn      = {1951-6355},
  year      = {2008},
  abstract  = {When we fixate our gaze on a stable object, our eyes move continuously with extremely small involuntary and autonomic movements, that even we are unaware of during their occurrence. One of the roles of these fixational eye movements is to prevent the adaptation of the visual system to continuous illumination and inhibit fading of the image. These random, small movements are restricted at long time scales so as to keep the target at the centre of the field of view. In addition, the synchronisation properties between both eyes are related to binocular coordination in order to provide stereopsis. We investigated the roles of different time scale behaviours, especially how they are expressed in the different spatial directions (vertical versus horizontal). We also tested the synchronisation between both eyes. Results show different scaling behaviour between horizontal and vertical movements. When the small ballistic movements, i.e., microsaccades, are removed, the scaling behaviour in both axes becomes similar. Our findings suggest that microsaccades enhance the persistence at short time scales mostly in the horizontal component and much less in the vertical component. We also applied the phase synchronisation decay method to study the synchronisation between six combinations of binocular fixational eye movement components. We found that the vertical-vertical components of right and left eyes are significantly more synchronised than the horizontal-horizontal components. These differences may be due to the need for continuously moving the eyes in the horizontal plane in order to match the stereoscopic image for different viewing distances.},
  language  = {en}
}