TY - INPR A1 - Witt, Annette A1 - Neiman, Alexander A1 - Kurths, Jürgen T1 - Characterizing the dynamics of stochastic bistable systems by measures of complexity N2 - The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum. T3 - NLD Preprints - 36 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14556 ER - TY - INPR A1 - Witt, Annette A1 - Kurths, Jürgen A1 - Krause, F. A1 - Fischer, K. T1 - On the validity of a model for the reversals of the Earth‘s magnetic field N2 - We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information. T3 - NLD Preprints - 4 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13460 ER - TY - INPR A1 - Kurths, Jürgen A1 - Voss, A. A1 - Witt, Annette A1 - Saparin, P. A1 - Kleiner, H. J. A1 - Wessel, Niels T1 - Quantitative analysis of heart rate variability N2 - In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. T3 - NLD Preprints - 5 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13470 ER - TY - INPR A1 - Thiessenhusen, Kai-Uwe A1 - Esposito, Larry W. A1 - Kurths, Jürgen A1 - Spahn, Frank T1 - Detection of hidden resonances in Saturn's B-ring N2 - The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances. T3 - NLD Preprints - 13 KW - Planetary Rings Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13618 ER - TY - INPR A1 - Voss, Henning A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis N2 - Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record. T3 - NLD Preprints - 28 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14083 ER - TY - INPR A1 - Engbert, Ralf A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Rosenblum, Mikhael 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. T3 - NLD Preprints - 41 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14380 ER - TY - INPR A1 - Guasti, Giovanna A1 - Engbert, Ralf A1 - Krampe, Ralf T. A1 - Kurths, Jürgen T1 - Phase transitions, complexity, and stationarity in the production of polyrhythms N2 - Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook T3 - NLD Preprints - 57 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14933 ER - TY - INPR A1 - Pikovskij, Arkadij A1 - Zaks, Michael A. A1 - Feudel, Ulrike A1 - Kurths, Jürgen T1 - Singular continuous spectra in dissipative dynamics N2 - We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique. T3 - NLD Preprints - 15 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787 ER - TY - INPR A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij A1 - Scheffczyk, Christian T1 - Roughening interfaces in deterministic dynamics N2 - Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface. T3 - NLD Preprints - 3 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13447 ER -