Biomedical subjects

Jürgen Kurths

Publications and source records attributed to Jürgen Kurths.

At least 19 recordsLinked to original sources

PubMed2006

Phase-flip bifurcation induced by time delay.

We present a general bifurcation in the synchronized dynamics of time-delay-coupled nonlinear oscillators. The relative phase between the oscillators jumps from zero to pi as a function of the coupling; this phase-flip bifurcation is accompanied by a discontinuous change in the frequency of the synchronized oscillators. This phenomenon is of broad relevance, being observed in regimes of oscillator death as well as in periodic, quasiperiodic, and chaotic dynamics. Time-delay coupling is necessary for the phase-flip bifurcation. We illustrate the phenomenon, and present analytical results for paradigmatic nonlinear systems. Possible applications are discussed.

Journal Article↗

PubMed2006

Partial phase synchronization for multivariate synchronizing systems.

Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated.

Journal Article↗

PubMed2006

Dynamical weights and enhanced synchronization in adaptive complex networks.

Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks.

Journal Article↗

PubMed2006

Large-scale dimension densities for heart rate variability analysis.

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.

Atrial Fibrillation↗

PubMed2006

Nonlinear additive autoregressive model-based analysis of short-term heart rate variability.

In this contribution we test the hypothesis that nonlinear additive autoregressive model-based data analysis improves the diagnostic ability based on short-term heart rate variability. For this purpose, a nonlinear regression approach, namely, the maximal correlation method is applied to the data of 37 patients with dilated cardiomyopathy as well as of 37 age- and sex-matched healthy subjects. We find that this approach is a powerful tool in discriminating both groups and promising for further model-based analyses.

Algorithms↗

PubMed2006

Universality in the synchronization of weighted random networks.

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters.

Journal Article↗

PubMed2006

Hierarchical synchronization in complex networks with heterogeneous degrees.

We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function.

Journal Article↗

PubMed2006

Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators.

We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models.

Algorithms↗

PubMed2006

Segmentation of bone CT images and assessment of bone structure using measures of complexity.

A nondestructive and noninvasive method for numeric characterization (quantification) of the structural composition of human bone tissue has been developed and tested. In order to quantify and to compare the structural composition of bones from 2D computed tomography (CT) images acquired at different skeletal locations, a series of robust, versatile, and adjustable image segmentation and structure assessment algorithms were developed. The segmentation technique facilitates separation from cortical bone and standardizes the region of interest. The segmented images were symbol-encoded and different aspects of the bone structural composition were quantified using six different measures of complexity. These structural examinations were performed on CT images of bone specimens obtained at the distal radius, humeral mid-diaphysis, vertebral body, femoral head, femoral neck, proximal tibia, and calcaneus. In addition, the ability of the noninvasive and nondestructive measures of complexity to quantify trabecular bone structure was verified by comparing them to conventional static histomorphometry performed on human fourth lumbar vertebral bodies. Strong correlations were established between the measures of complexity and the histomorphometric parameters except for measures expressing trabecular thickness. Furthermore, the ability of the measures of complexity to predict vertebral bone strength was investigated by comparing the outcome of the complexity analysis of the CT images with the results of a biomechanical compression test of the third lumbar vertebral bodies from the same population as used for histomorphometry. A multiple regression analysis using the proposed measures including structure complexity index, structure disorder index, trabecular network index, index of a global ensemble, maximal L-block, and entropy of x-ray attenuation distribution revealed an excellent relationship (r=0.959, r2=0.92) between the measures of complexity and compressive bone strength. In conclusion, the image segmentation techniques and the assessment of bone architecture by measures of complexity have been successfully applied to analyze high-resolution peripheral quantitative computed tomography (pQCT) and CT images obtained from the distal radius, humeral mid-diaphysis, third and fourth lumbar vertebral bodies, proximal femur, proximal tibia, and calcaneus. The proposed approach is of broad interest as it can be applied for the quantification of structures and textures originating from different imaging modalities in other fields of science.

Aged↗

PubMed2006

Normalized correlation dimension for heart rate variability analysis.

In this paper we use the concept of large-scale dimension densities to analyze heart rate variability data. This method uses a normalized Grassberger-Procaccia algorithm and estimates the dimension in the rather large scales of the system. This enables us to analyze very short data. First we re-analyze data from the CIC 2002 challenge and can completely distinguish between real data and computer-generated data using only one parameter. We then analyze unfiltered data for 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects, and 18 young healthy subjects. This method can completely separate the AF group from the other groups and the CHF patients show significant differences compared to the young and elderly healthy volunteers. Furthermore, differences are evident in the dimensionality between day and night for healthy persons, but not for the CHF patients. Finally, the results are compared to standard heart rate variability parameters.

Adult↗

PubMed2005

Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis.

We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event-related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so.

Algorithms↗

PubMed2005

Synchronized chaotic intermittent and spiking behavior in coupled map chains.

We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.

Journal Article↗

PubMed2005

Measuring phase synchronization of superimposed signals.

Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls.

Models, Biological↗

PubMed2005

Additive nonparametric reconstruction of dynamical systems from time series.

We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential.

Journal Article↗

PubMed2005

Network synchronization, diffusion, and the paradox of heterogeneity.

Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength. Here we offer a solution to this apparent paradox. Our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states. We show that, for a given degree distribution, the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum. This enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size. Numerical verification of the main results is provided for representative classes of small-world and scale-free networks.

Journal Article↗

PubMed2005

Synchronized firing of FitzHugh-Nagumo neurons by noise.

We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons.

Action Potentials↗

PubMed2004

Synchronization of two interacting populations of oscillators.

We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment, and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.

Adaptation, Physiological↗

PubMed2004

Predicting phase synchronization in a spiking chaotic CO2 laser.

An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments.

Journal Article↗