TY - GEN
A1 - Allefeld, Carsten
A1 - Kurths, Jürgen
T1 - Testing for phase synchronization
N2 - We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 071
Y1 - 2004
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20091
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 - paper 013
KW - Planetary Rings
Y1 - 1995
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13618
ER -
TY - GEN
A1 - Koseska, Aneta
A1 - Zaikin, Alexey
A1 - Kurths, Jürgen
A1 - García-Ojalvo, Jordi
T1 - Timing cellular decision making under noise via cell-cell communication
N2 - Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 148
Y1 - 2009
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45260
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 - paper 041
Y1 - 1997
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14380
ER -
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 - paper 036
Y1 - 1997
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14556
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 - paper 057
Y1 - 2000
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14933
ER -
TY - INPR
A1 - Pikovsky, Arkady S.
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 - paper 015
Y1 - 1995
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787
ER -
TY - INPR
A1 - Kurths, Jürgen
A1 - Voss, A.
A1 - Witt, Annette
A1 - Saparin, P.
A1 - Kleiner, H. J.
A1 - Wessel, N.
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 - paper 005
Y1 - 1994
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13470
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 - paper 004
Y1 - 1994
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13460
ER -
TY - INPR
A1 - Kurths, Jürgen
A1 - Pikovsky, Arkady S.
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 - paper 003
Y1 - 1994
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13447
ER -