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Search Results: 1 - 10 of 297572 matches for " Jürgen Kurths "
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Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems
Norbert Marwan,Jürgen Kurths
Physics , 2015, DOI: 10.1063/1.4916924
Abstract: We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.
Synchronization of two interacting populations of oscillators
Ernest Montbrió,Jürgen Kurths,Bernd Blasius
Physics , 2004, DOI: 10.1103/PhysRevE.70.056125
Abstract: 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 (Okuda and Kuramoto, 1991). 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.
Role of delay in the mechanism of cluster formation
Aradhana Singh,Sarika Jalan,Jürgen Kurths
Physics , 2012, DOI: 10.1103/PhysRevE.87.030902
Abstract: We study the role of delay in phase synchronization and phenomena responsible for cluster formation in delayed coupled maps on various networks. Using numerical simulations, we demonstrate that the presence of delay may change the mechanism of unit to unit interaction. At weak coupling values, same parity delays are associated with the same phenomenon of cluster formation and exhibit similar dynamical evolution. Intermediate coupling values yield rich delay-induced driven cluster patterns. A Lyapunov function analysis sheds light on the robustness of the driven clusters observed for delayed bipartite networks. Our results reveal that delay may lead to a completely different relation, between dynamical and structural clusters, than observed for the undelayed case.
Recurrence Plots 25 years later -- gaining confidence in dynamical transitions
Norbert Marwan,Stefan Schinkel,Jürgen Kurths
Physics , 2013, DOI: 10.1209/0295-5075/101/20007
Abstract: Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.
Analysing spatially extended high-dimensional dynamics by recurrence plots
Norbert Marwan,Jürgen Kurths,Saskia Foerster
Physics , 2014, DOI: 10.1016/j.physleta.2015.01.013
Abstract: Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
Revival of oscillation from mean-field-induced death: Theory and experiment
Debarati Ghosh,Tanmoy Banerjee,Jürgen Kurths
Physics , 2015, DOI: 10.1103/PhysRevE.92.052908
Abstract: The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in [Zou et al. Nature Commun. 6:7709, 2015], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has {\it two control parameters}, namely the {\it density of the mean-field} and the {\it feedback parameter} that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean-field is capable of inducing rhythmicity even in the presence of complete diffusion, which is an unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the {\it first} experimental observation of revival of oscillation from the mean-field--induced oscillation suppression state that supports our theoretical results.
Identifying Controlling Nodes in Neuronal Networks in Different Scales
Yang Tang, Huijun Gao, Wei Zou, Jürgen Kurths
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0041375
Abstract: Recent studies have detected hubs in neuronal networks using degree, betweenness centrality, motif and synchronization and revealed the importance of hubs in their structural and functional roles. In addition, the analysis of complex networks in different scales are widely used in physics community. This can provide detailed insights into the intrinsic properties of networks. In this study, we focus on the identification of controlling regions in cortical networks of cats’ brain in microscopic, mesoscopic and macroscopic scales, based on single-objective evolutionary computation methods. The problem is investigated by considering two measures of controllability separately. The impact of the number of driver nodes on controllability is revealed and the properties of controlling nodes are shown in a statistical way. Our results show that the statistical properties of the controlling nodes display a concave or convex shape with an increase of the allowed number of controlling nodes, revealing a transition in choosing driver nodes from the areas with a large degree to the areas with a low degree. Interestingly, the community Auditory in cats’ brain, which has sparse connections with other communities, plays an important role in controlling the neuronal networks.
Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations
Anna Zakharova,Jürgen Kurths,Tatyana Vadivasova,Aneta Koseska
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0019696
Abstract: The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.
Unraveling gene regulatory networks from time-resolved gene expression data -- a measures comparison study
Sabrina Hempel, Aneta Koseska, Zoran Nikoloski, Jürgen Kurths
BMC Bioinformatics , 2011, DOI: 10.1186/1471-2105-12-292
Abstract: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study.Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.Recent evidence from fully-sequenced genomes suggests that organismal complexity arises more from the elaborate regulation of gene expression than from the genome size itself [1]. It
Exploring Brain Function from Anatomical Connectivity
Gorka Zamora-López,Changsong Zhou,Jürgen Kurths
Frontiers in Neuroscience , 2011, DOI: 10.3389/fnins.2011.00083
Abstract: The intrinsic relationship between the architecture of the brain and the range of sensory and behavioral phenomena it produces is a relevant question in neuroscience. Here, we review recent knowledge gained on the architecture of the anatomical connectivity by means of complex network analysis. It has been found that cortico-cortical networks display a few prominent characteristics: (i) modular organization, (ii) abundant alternative processing paths, and (iii) the presence of highly connected hubs. Additionally, we present a novel classification of cortical areas of the cat according to the role they play in multisensory connectivity. All these properties represent an ideal anatomical substrate supporting rich dynamical behaviors, facilitating the capacity of the brain to process sensory information of different modalities segregated and to integrate them toward a comprehensive perception of the real world. The results here exposed are mainly based on anatomical data of cats’ brain, but further observations suggest that, from worms to humans, the nervous system of all animals might share these fundamental principles of organization.
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