TY - JOUR A1 - Wessel, Niels A1 - Marwan, Norbert A1 - Meyerfeldt, Udo A1 - Schirdewan, Alexander A1 - Kurths, Jürgen T1 - Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia N2 - Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the Y1 - 2001 UR - http://link.springer.de/link/service/series/0558/bibs/2199/21990295.htm ER - TY - JOUR A1 - Rosenblum, Michael A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij T1 - Comment on "Phase synchronization in discrete chaotic systems" N2 - Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful. Y1 - 2001 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - Detecting direction of coupling in interacting oscillators N2 - We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling. Y1 - 2001 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Neumann, Eireen T1 - Comment on "Simple approach to the creation of a strange nonchaotic attractor in any chaotic system" N2 - We address the problem of existence of strange nonchaotic attractors (SNAs) in quasiperiodically forced dynamical systems. Recently, Shuai and Wong [Phys. Rev. E 59, 5338 (1999)] suggested a universal method for constructing a SNA in an arbitrary system possessing chaos. We demonstrate here that, in general, this method fails. For arbitrary systems, it gives a SNA only in a vicinity of transition to chaos. We discuss also a special example, where the method by Shuai and Wong indeed produces a SNA. Y1 - 2001 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - Comment on "Intermittency in chaotic rotations" N2 - Lai et al. [Phys. Rev. E 62, R29 (2000)] claim that the angular velocity of the phase point moving along the chaotic trajectory in a properly chosen projection (the instantaneous frequency) is intermittent. Using the same examples, namely the Rössler and the Lorenz systems, we show the absence of intermittency in the dynamics of the instantaneous frequency.This is confirmed by demonstrating that the phase dynamics exhibits normal diffusion. We argue that the nonintermittent behavior is generic. Y1 - 2001 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Popovych, Orest A1 - Maistrenko, Yu T1 - Resolving Clusters in Chaotic Ensembles of Globally Coupled Identical Oscillators N2 - Clustering in ensembles of globally coupled identical chaotic oscillators is reconsidered using a twofold approach. Stability of clusters towards "emanation" of the elements is described with the evaporation Lyapunov exponents. It appears that direct numerical simulations of ensembles often lead to spurious clusters that have positive evaporation exponents, due to a numerical trap. We propose a numerical method that surmounts the spurious clustering. We also demonstrate that clustering can be very sensitive to the number of elements in the ensemble. Y1 - 2001 ER - TY - JOUR A1 - Topaj, Dmitri A1 - Kye, W.-H A1 - Pikovskij, Arkadij T1 - Transition to Coherence in Populations of Coupled Chaotic Oscillators: A Linear Response Approach N2 - We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics. Y1 - 2001 ER - TY - JOUR A1 - Tsimring, L. S. A1 - Pikovskij, Arkadij T1 - Noise-Induced Dynamics in Bistable Systems with Delay N2 - Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. Analytical solutions for the autocorrelation function and the power spectrum have been found. The power spectrum has a peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics. Y1 - 2001 ER - TY - JOUR A1 - Wagner, Annekatrin A1 - Kamjunke, Norbert T1 - Reduction of the filtration rate of Daphnia galeata by dissolved photosynthetic products of edible phytoplankton N2 - The filtration rate of Daphnia galeata was determined in in situ experiments in Bautzen Reservoir and in laboratory experiments, where daphnids were exposed to filtrates that previously contained either natural phytoplankton or cultured eukaryotic algae (Scenedesmus obliquus or Asterionella formosa), respectively. Individual filtration rate (FR) was measured using fluorescent beads, taking into account ingested beads in the gut only. Compared to heated control treatments (100°C), dissolved compounds released by the nutritious cultured algae during the preconditioning phase or by the natural phytoplankton assemblages from Bautzen Reservoir strongly reduced the filtration rate of D. galeata (down to 60 %). Heating deactivated these dissolved compounds. A significant correlation was found between primary production measured in situ and the reduction of FR in the filtrate of reservoir water, indicating that extra- cellular products released during photosynthesis triggered the reduction of the filtration rate. The ratio of ingested to collected beads was used to quantify the proportion of food, which was not only collected but passed the mouth of D. galeata. The ratio of ingestion to collection was compared between filtered and unfiltered reservoir water both media identical with respect to the concentration of dissolved compounds, whereas other factors (e. g. food concentration, temperature, filtration rate) were different. The changes in this ratio between filtered and unfiltered reservoir water suggest that D. galeata is capable of a chemosensory control of the ingestion behaviour by detecting external metabolites. Y1 - 2001 ER - TY - JOUR A1 - Kamjunke, Norbert A1 - Mehner, Thomas T1 - Coupling the microbial food web with fish : are bacteria attached to cyanobacteria an important food source for underyearling roach? N2 - 1. After observing that juvenile roach fed intensively on cyanobacteria and that cyanobacteria were densely colonized by heterotrophic bacteria, we tested whether the bacteria are used by underyearling roach and the extent to which they contribute to the energy requirements of the fish. 2. We radiolabeled attached bacteria in a natural cyanobacterial suspension, fed the fish with these particles, and estimated their assimilation by roach. Biomass of attached bacteria on cyanobacteria increased with the proportion of the cyanobacterium Microcystis in total cyanobacteria. Biomass-specific thymidine incorporation of attached bacteria was higher than that of free bacteria. 3. In feeding experiments, we detected assimilation of bacterial biomass into muscle tissue of underyearling roach. Fish consumed Microcystis to a lesser extent compared to Aphanizomenon but assimilation of attached bacteria was higher when roach fed on Microcystis due to the higher biomass of epibacteria on this cyanobacterium. However, biomass of attached bacteria was too low to be an important food source for underyearling roach. 4. We conclude that assimilation of epibacteria from cyanobacteria cannot explain the success of roach in eutrophic lakes. Y1 - 2001 ER -