arXiv subjects

Reik V. Donner

Publications and source records attributed to Reik V. Donner.

At least 37 records · Page 2Linked to original sources

arXiv2018

Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index

Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity measures provides a promising approach for identifying the underlying processes and associated time-scales. Here, we apply a suite of characteristics from recurrence quantification analysis (RQA) and recurrence network analysis (RNA) in order to unveil some key nonlinear features of the hourly Disturbance storm-time (Dst) index during periods with magnetic storms and such of normal variability. Our results demonstrate that recurrence-based measures can serve as excellent tracers for changes in the dynamical complexity along non-stationary records of geomagnetic activity. In particular, trapping time (characterizing the typical length of "laminar phases" in the observed dynamics) and recurrence network transitivity (associated with the number of the system's effective dynamical degrees of freedom) allow for a very good discrimination between magnetic storm and quiescence phases. In general, some RQA and RNA characteristics distinguish between storm and non-storm times equally well or even better than other previously considered nonlinear characteristics like Hurst exponent or symbolic dynamics based entropy concepts. Our results point to future potentials of recurrence characteristics for unveiling temporal changes in the dynamical complexity of the magnetosphere.

physics.ao-ph↗

arXiv2018

Recurrence based quantification of dynamical complexity in the Earth's magnetosphere at geospace storm timescales

Magnetic storms are the most prominent global manifestations of out-of-equilibrium magnetospheric dynamics. Investigating the dynamical complexity exhibited by geomagnetic observables can provide valuable insights into relevant physical processes as well as temporal scales associated with this phenomenon. In this work, we utilize several innovative data analysis techniques enabling a quantitative nonlinear analysis of the nonstationary behavior of the disturbance storm time (Dst) index together with some of the main drivers of its temporal variability, the $VB_{South}$ electric field component, the vertical component of the interplanetary magnetic field, $B_z$, and the dynamic pressure of the solar wind, $P_{dyn}$. Using recurrence quantification analysis (RQA) and recurrence network analysis (RNA), we obtain several complementary complexity measures that serve as markers of different physical processes underlying quiet and storm time magnetospheric dynamics. Specifically, our approach discriminates the magnetospheric activity in response to external (solar wind) forcing from primarily internal variability and provides a physically meaningful classification of magnetic storm periods based on observations made at the Earth's surface. In this regard, the proposed methodology could provide a relevant step towards future improved space weather and magnetic storm forecasts.

physics.space-ph↗

arXiv2018

Phase space reconstruction for non-uniformly sampled noisy time series

Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's higher-dimensional phase space can be crucial for further analyses. In this study, we systematically compare the methods of time delay embedding and differential embedding for phase space reconstruction. Differential embedding relates the system's higher-dimensional coordinates to the derivatives of the measured time series. For implementation, this requires robust and efficient algorithms to estimate derivatives from noisy and possibly non-uniformly sampled data. For this purpose, we consider several approaches: (i) central differences adapted to irregular sampling, (ii) a generalized version of discrete Legendre coordinates and (iii) the concept of Moving Taylor Bayesian Regression. We evaluate the performance of differential and time delay embedding by studying two paradigmatic model systems - the Lorenz and the Rössler system. More precisely, we compare geometric properties of the reconstructed attractors to those of the original attractors by applying recurrence network analysis. Finally, we demonstrate the potential and the limitations of using the different phase space reconstruction methods in combination with windowed recurrence network analysis for inferring information about past climate variability. This is done by analyzing two well-studied paleoclimate data sets from Ecuador and Mexico. We find that studying the robustness of the results when varying the analysis parameters is an unavoidable step in order to make well-grounded statements on climate variability and to judge whether a data set is suitable for this kind of analysis.

physics.data-an↗

arXiv2017

Global teleconnectivity structures of the El Niño-Southern Oscillation and large volcanic eruptions -- An evolving network perspective

Recent work has provided ample evidence that global climate dynamics at time-scales between multiple weeks and several years can be severely affected by the episodic occurrence of both, internal (climatic) and external (non-climatic) perturbations. Here, we aim to improve our understanding on how regional to local disruptions of the "normal" state of the global surface air temperature field affect the corresponding global teleconnectivity structure. Specifically, we present an approach to quantify teleconnectivity based on different characteristics of functional climate network analysis. Subsequently, we apply this framework to study the impacts of different phases of the El Niño-Southern Oscillation (ENSO) as well as the three largest volcanic eruptions since the mid 20th century on the dominating spatiotemporal co-variability patterns of daily surface air temperatures. Our results confirm the existence of global effects of ENSO which result in episodic breakdowns of the hierarchical organization of the global temperature field. This is associated with the emergence of strong teleconnections. At more regional scales, similar effects are found after major volcanic eruptions. Taken together, the resulting time-dependent patterns of network connectivity allow a tracing of the spatial extents of the dominating effects of both types of climate disruptions. We discuss possible links between these observations and general aspects of atmospheric circulation.

physics.ao-ph↗

arXiv2017

Zealotry Effects on Opinion Dynamics in the Adaptive Voter Model

The adaptive voter model has been widely studied as a conceptual model for opinion formation processes on time-evolving social networks. Past studies on the effect of zealots, i.e. nodes aiming to spread their fixed opinion throughout the system, only considered the voter model on a static network. Here, we extend the study of zealotry to the case of an adaptive network topology co-evolving with the state of the nodes and investigate opinion spreading induced by zealots depending on their initial density and connectedness. Numerical simulations reveal that below the fragmentation threshold a low density of zealots is sufficient to spread their opinion to the whole network. Beyond the transition point, zealots must exhibit an increased degree as compared to ordinary nodes for an efficient spreading of their opinion. We verify the numerical findings using a mean-field approximation of the model yielding a low-dimensional set of coupled ordinary differential equations. Our results imply that the spreading of the zealot opinion in the adaptive voter model is strongly dependent on the rate of link rewiring and the average degree of normal nodes in comparison with that of the zealots. In order to avoid a complete dominance of the zealots' opinion, there are two possible strategies for the remaining nodes: adjusting the rate of rewiring and/or the number of connections with other nodes, respectively.

physics.soc-ph↗

arXiv2017

Mapping and discrimination of networks in the complexity-entropy plane

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here, we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged per-node entropic measure characterizing the network's information content and the associated Jenson-Shannon divergence as a measure of disequilibrium. We study 29 real world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g, transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.

physics.data-an↗

arXiv2017

Rewiring hierarchical scale-free networks: Influence on synchronizability and topology

Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barabási \etal, Physica A, 299, 3 (2001)] and pseudofractal scale-free [S. N. Dorogovtsev \etal, Phy. Rev. E, 65, 6 (2002)] networks constitute notable models which simultaneously incorporate the aforementioned properties. The rules governing the formation of such networks are completely deterministic. However, real-world networks are presumably neither completely deterministic, nor perfectly hierarchical. Therefore, we suggest here perfectly hierarchical scale-free networks with randomly rewired edges as better representatives of practical networked systems. In particular, we preserve the scale-free degree distribution of the various deterministic networks but successively relax the hierarchical structure while rewiring them. We utilize the framework of master stability function in investigating the synchronizability of dynamical systems coupled on such rewired networks. Interestingly, this reveals that the process of rewiring is capable of significantly enhancing, as well as, deteriorating the synchronizability of the resulting networks. We investigate the influence of rewiring edges on the topological properties of the rewired networks and, in turn, their relation to the synchronizability of the respective topologies. Finally, we compare the synchronizability of deterministic scale-free and pseudofractcal scale-free networks with that of random scale-free networks (generated using the classical Barabási-Albert model of growth and preferential attachment) and find that the latter ones promote synchronizability better than their deterministic counterparts.

physics.soc-ph↗

arXiv2017

Recovery time after localized perturbations in complex dynamical networks

Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases before the system returns to synchrony, following a random perturbation to the dynamical state of any particular node of the network. We address this issue here by proposing the framework of \emph{single-node recovery time} (SNRT) which provides an estimate of the relative time scales underlying the transient dynamics of the nodes of a network during its restoration to synchrony. We utilize this in differentiating the particularly \emph{slow} nodes of the network from the relatively \emph{fast} nodes, thus identifying the critical nodes which when perturbed lead to significantly enlarged recovery time of the system before resuming synchronized operation. Further, we reveal explicit relationships between the SNRT values of a network, and its \emph{global relaxation time} when starting all the nodes from random initial conditions. We employ the proposed concept for deducing microscopic relationships between topological features of nodes and their respective SNRT values. The framework of SNRT is further extended to a measure of resilience of the different nodes of a networked dynamical system. We demonstrate the potential of SNRT in networks of Rössler oscillators on paradigmatic topologies and a model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics illustrating the conceivable practical applicability of the proposed concept.

nlin.CD↗

arXiv2016

Multi-node basin stability in complex dynamical networks

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) (Menck et al., Nature Physics 9, 89 (2013)), we propose here the general framework of \emph{multi-node basin stability} for gauging global stability and robustness of networked dynamical systems in response to non-local perturbations simultaneously affecting multiple nodes of a system. The framework of multi-node BS provides an estimate of the critical number of nodes which when simultaneously perturbed, significantly reduces the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multi-node BS can also be utilized for probing the influence of spatially localised perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multi-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.

nlin.CD↗

arXiv2016

A perturbative approach to Lagrangian flow networks

Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals or volcanic aerosols.

physics.flu-dyn↗

arXiv2016

Hierarchical structures in Northern Hemispheric extratropical winter ocean-atmosphere interactions

In recent years extensive studies on the Earth's climate system have been carried out by means of advanced complex network statistics. The great majority of these studies, however, have been focusing on investigating correlation structures within single climatic fields directly on or parallel to the Earth's surface. Here, we develop a novel approach of node weighted coupled network measures to study correlations between ocean and atmosphere in the Northern Hemisphere extratropics and construct 18 coupled climate networks, each consisting of two subnetworks. In all cases, one subnetwork represents monthly sea-surface temperature (SST) anomalies, while the other is based on the monthly geopotential height (HGT) of isobaric surfaces at different pressure levels covering the troposphere as well as the lower stratosphere. The weighted cross-degree density proves to be consistent with the leading coupled pattern obtained from maximum covariance analysis. Network measures of higher order allow for a further analysis of the correlation structure between the two fields and consistently indicate that in the Northern Hemisphere extratropics the ocean is correlated with the atmosphere in a hierarchical fashion such that large areas of the ocean surface correlate with multiple statistically dissimilar regions in the atmosphere. Ultimately we show that, this observed hierarchy is linked to large-scale atmospheric variability patterns, such as the Pacific North American pattern, forcing the ocean on monthly time scales.

physics.ao-ph↗

arXiv2016

A climate network-based index to discriminate different types of El Niño and La Niña

El Niño exhibits distinct Eastern Pacific (EP) and Central Pacific (CP) types which are commonly, but not always consistently, distinguished from each other by different signatures in equatorial climate variability. Here, we propose an index based on evolving climate networks to objectively discriminate between both flavors by utilizing a scalar-valued evolving climate network measure that quantifies spatial localization and dispersion in El Niño's associated teleconnections. Our index displays a sharp peak (high localization) during EP events, whereas during CP events (larger dispersion) it remains close to the baseline observed during normal periods. In contrast to previous classification schemes, our approach specifically account for El Niño's global impacts. We confirm recent El Niño classifications for the years 1951 to 2014 and assign types to those cases were former works yielded ambiguous results. Ultimately, we study La Niña episodes and demonstrate that our index provides a similar discrimination into two types.

physics.data-an↗

arXiv2016

Edge anisotropy and the geometric perspective on flow networks

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.

physics.flu-dyn↗

arXiv2016

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.

physics.soc-ph↗

arXiv2016

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.

physics.data-an↗

arXiv2016

Event coincidence analysis for quantifying statistical interrelationships between event time series: on the role of flood events as possible triggers of epidemic outbreaks

Studying event time series is a powerful approach for analyzing the dynamics of complex dynamical systems in many fields of science. In this paper, we describe the method of event coincidence analysis to provide a framework for quantifying the strength, directionality and time lag of statistical interrelationships between event series. Event coincidence analysis allows to formulate and test null hypotheses on the origin of the observed interrelationships including tests based on Poisson processes or, more generally, stochastic point processes with a prescribed inter-event time distribution and other higher-order properties. Applying the framework to country-level observational data yields evidence that flood events have acted as triggers of epidemic outbreaks globally since the 1950s. Facing projected future changes in the statistics of climatic extreme events, statistical techniques such as event coincidence analysis will be relevant for investigating the impacts of anthropogenic climate change on human societies and ecosystems worldwide.

physics.soc-ph↗

arXiv2016

Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: a Lagrangian flow network perspective

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that characterizes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic (ROC) analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.

nlin.CD↗

arXiv2016

Disentangling regular and chaotic motion in the standard map using complex network analysis of recurrences in phase space

Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently attracted much interest for discriminating qualitatively different types of dynamics in terms of measures of complexity, dynamical invariants, or even structural characteristics of the underlying attractor's geometry in phase space. Here, we demonstrate that the latter approach also provides a corresponding distinction between different co-existing dynamical regimes of the standard map, a paradigmatic example of a low-dimensional conservative system. Specifically, we show that the recently developed approach of recurrence network analysis provides potentially useful geometric characteristics distinguishing between regular and chaotic orbits. We find that chaotic orbits in an intermittent laminar phase (commonly referred to as sticky orbits) have a distinct geometric structure possibly differing in a subtle way from those of regular orbits, which is highlighted by different recurrence network properties obtained from relatively short time series. Thus, this approach can help discriminating regular orbits from laminar phases of chaotic ones, which presents a persistent challenge to many existing chaos detection techniques.

nlin.CD↗