TY - JOUR A1 - Surovyatkina, E. D. A1 - Kravtsov, Y. A. A1 - Kurths, Jürgen T1 - Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking N2 - We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Shabunin, A. A1 - Astakhov, Vladimir V. A1 - Kurths, Jürgen T1 - Quantitative analysis of chaotic synchronization by means of coherence N2 - We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Saparin, P. I. A1 - Thomsen, J. S. A1 - Prohaska, Steffen A1 - Zaikin, Alexei A1 - Kurths, Jürgen A1 - Hege, H. C. A1 - Gowin, W. T1 - Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity N2 - Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved Y1 - 2005 SN - 0094-5765 ER - TY - JOUR A1 - Sitz, Andre A1 - Schwarz, Udo A1 - Kurths, Jürgen T1 - The unscented Kalman filter : a powerful tool for data analysis Y1 - 2004 ER - TY - JOUR A1 - Raab, Corinna A1 - Wessel, Niels A1 - Schirdewan, Alexander A1 - Kurths, Jürgen T1 - Large-scale dimension densities for heart rate variability analysis N2 - In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.041907 SN - 1539-3755 ER - TY - JOUR A1 - Anishchenko, Vadim S. A1 - Nikolaev, S A1 - Kurths, Jürgen T1 - Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions N2 - We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.056202 SN - 1539-3755 ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Hwang, Dong-Uk A1 - Chavez, Mario A1 - Amann, Andreas A1 - Kurths, Jürgen A1 - Pecora, Louis M. T1 - Synchronization in dynamical networks : evolution along commutative graphs N2 - Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.74.016102 SN - 1539-3755 ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen T1 - Spurious structures in recurrence plots induced by embedding N2 - In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay Y1 - 2006 U6 - https://doi.org/10.1007/s11071-006-2010-9 ER - TY - JOUR A1 - Li, Changpin A1 - Sun, Weigang A1 - Kurths, Jürgen T1 - Synchronization of complex dynamical networks with time delays N2 - In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2005.07.007 SN - 0378-4371 ER - TY - JOUR A1 - Schmidt, G. A1 - Zamora-Lopez, Gorka A1 - Kurths, Jürgen T1 - Simulation of large scale cortical networks by individual neuron dynamics N2 - Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required. Y1 - 2010 U6 - https://doi.org/10.1142/S0218127410026149 SN - 0218-1274 ER -