TY - JOUR A1 - Herrmann, Carl J. J. A1 - Metzler, Ralf A1 - Engbert, Ralf T1 - A self-avoiding walk with neural delays as a model of fixational eye movements JF - Scientific reports N2 - Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-13489-8 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Makarava, Natallia A1 - Bettenbühl, Mario A1 - Engbert, Ralf A1 - Holschneider, Matthias T1 - Bayesian estimation of the scaling parameter of fixational eye movements JF - epl : a letters journal exploring the frontiers of physics N2 - In this study we re-evaluate the estimation of the self-similarity exponent of fixational eye movements using Bayesian theory. Our analysis is based on a subsampling decomposition, which permits an analysis of the signal up to some scale factor. We demonstrate that our approach can be applied to simulated data from mathematical models of fixational eye movements to distinguish the models' properties reliably. Y1 - 2012 U6 - https://doi.org/10.1209/0295-5075/100/40003 SN - 0295-5075 VL - 100 IS - 4 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Kurths, Jürgen A1 - Krampe, Ralf-Thomas A1 - Kliegl, Reinhold T1 - Nonlinear Phenomena in Polyrhythmic Hand Movements N2 - 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. Y1 - 1995 SN - 981-02-2689-6 ER - TY - JOUR A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Krampe, Ralf-Thomas A1 - Kurths, Jürgen A1 - Rosenblum, Michael A1 - Zaikin, Alexei A. T1 - Nonlinear Modelling of Polyrhythmic Hand Movements Y1 - 1996 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Rosenblum, Michael A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Krampe, Ralf-Thomas A1 - Kurths, Jürgen T1 - Modeling qualitative changes in bimanual movements Y1 - 1997 ER - TY - JOUR A1 - Schiek, Michael A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Kurths, Jürgen A1 - Krampe, Ralf-Thomas A1 - Kliegl, Reinhold A1 - Drepper, Friedhelm R. T1 - Symbolic dynamics of physiological synchronisation : examples from bimanual movements and cardiorespiratory interaction N2 - Key words: Nonlinear time series analysis, symbolic dynamics, phase transitions, physiological data, biological synchronization, production of polyrhythms, cardiorespiratory interaction, variation of control parameter Y1 - 1997 ER - TY - JOUR A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Engbert, Ralf A1 - Rosenblum, Michael A1 - Kurths, Jürgen A1 - Kliegl, Reinhold T1 - Tempo-induced transitions in polyrhythmic hand movements N2 - 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. Y1 - 1997 ER - TY - JOUR A1 - Engbert, Ralf A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Testing for unstable periodic orbits to characterize spatiotemporal dynamics Y1 - 1998 ER - TY - JOUR A1 - Schiek, Michael A1 - Drepper, Friedhelm R. A1 - Engbert, Ralf A1 - Suder, Katrin A1 - Abel, Hans-Henning T1 - Cardiorespiratory Synchronization N2 - The complex behaviour of cardiorespiratory dynamics is shown to be related to the interaction between several physiological oscillators. This study is based on electrocardiogram and respiratory flow data obtained from 3 different subjects during paced breathing at 10 different pacing cycle lengths ranging from 5 s to 12 s. Two different methods ideally suited for the analysis of synchronization pattern of coupled oscillators are applied: 1. Symbolic dynamics based on symbol coding adapted for the detection of respiratory modulation of cardiac parasympathetic activity discloses two regimes of different synchronization behaviour within the frequency area corresponding to the Arnold tongue of 1:1 frequency-locking between respiratory flow and respiratory heartbeat variation (respiratory sinus arrhythmia). 2. The analysis of the phase shift between respiratory flow and respiratory sinus arrhythmia indicates that synchronization is not a static but a dynamic phenomenon. The observed dependence of the phase shift on respiratory cycle length shows large inter-individual variation. These findings turn out to be further hints for the existence of an additional central oscillator in the frequency range of respiration interacting with the central respiratory oscillator driving mechanical respiration. Y1 - 1998 SN - 3-540-63481-9 ER - TY - JOUR A1 - Engbert, Ralf A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Kurths, Jürgen A1 - Kliegl, Reinhold T1 - Symbolic dynamics of bimanual production of polyrhythms N2 - We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system. Y1 - 2002 SN - 3-540- 63481-9 ER -