@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{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} } @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} } @article{BaptistaBohnKliegletal.2008, author = {Baptista, Murilo da Silva and Bohn, Christiane and Kliegl, Reinhold and Engbert, Ralf and Kurths, J{\"u}rgen}, title = {Reconstruction of eye movements during blinks}, issn = {1054-1500}, doi = {10.1063/1.2890843}, year = {2008}, language = {en} } @article{RomanoThielKurthsetal.2009, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Mergenthaler, Konstantin and Engbert, Ralf}, title = {Hypothesis test for synchronization : twin surrogates revisited}, issn = {1054-1500}, doi = {10.1063/1.3072784}, year = {2009}, abstract = {The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes.}, 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{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{SrinivasanSenthilkumarMuralietal.2011, author = {Srinivasan, K. and Senthilkumar, Dharmapuri Vijayan and Murali, K. and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen}, title = {Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {21}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {2}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.3591791}, pages = {11}, year = {2011}, abstract = {Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay tau(1) and coupling delay tau(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay tau(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.}, 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{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} }