Reik V. Donner

Recurrence networks—a novel paradigm for nonlinear time series analysis

This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.

Recurrence-based time series analysis by means of complex network methods

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.

Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution

Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35–3.15 Ma B.P.), (ii) Early Pleistocene (2.25–1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1–0.7 Ma B.P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.

Recurrence networks from multivariate signals for uncovering dynamic transitions of horizontal oil-water stratified flows

Characterizing the mechanism of drop formation at the interface of horizontal oil-water stratified flows is a fundamental problem eliciting a great deal of attention from different disciplines. We experimentally and theoretically investigate the formation and transition of horizontal oil-water stratified flows. We design a new multi-sector conductance sensor and measure multivariate signals from two different stratified flow patterns. Using the Adaptive Optimal Kernel Time-Frequency Representation (AOK TFR) we first characterize the flow behavior from an energy and frequency point of view. Then, we infer multivariate recurrence networks from the experimental data and investigate the cross-transitivity for each constructed network. We find that the cross-transitivity allows quantitatively uncovering the flow behavior when the stratified flow evolves from a stable state to an unstable one and recovers deeper insights into the mechanism governing the formation of droplets at the interface of stratified flows, a task that existing methods based on AOK TFR fail to work. These findings present a first step towards an improved understanding of the dynamic mechanism leading to the transition of horizontal oil-water stratified flows from a complex-network perspective.

Disentangling different types of El Nino episodes by evolving climate network analysis

Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network approach for characterizing the evolving correlation structure of the Earths climate system based on reanalysis data for surface air temperatures. We provide a detailed study of the temporal variability of several global climate network characteristics. Based on a simple conceptual view of red climate networks (i.e., networks with a comparably low number of edges), we give a thorough interpretation of our evolving climate network characteristics, which allows a functional discrimination between recently recognized different types of El Niño episodes. Our analysis provides deep insights into the Earths climate system, particularly its global response to strong volcanic eruptions and large-scale impacts of different phases of the El Niño Southern Oscillation.

Visibility graph analysis of geophysical time series: Potentials and possible pitfalls

Recently, complex network approaches to time series analysis have been developed and successfully applied to geophysical records. In this paper, the visibility graph approach is re-considered, which has been found useful as an alternative tool for describing the fractal properties of a time series. The interpretation of various graph-theoretical measures in the context of visibility graphs, their mutual interdependence, and their sensitivity in the presence of missing values and uncertainties (posing typical challenges in geophysical time series analysis) are thoroughly discussed. The obtained results are illustrated for some exemplary records from different fields of geosciences.

Armed-conflict risks enhanced by climate-related disasters in ethnically fractionalized countries

Significance Ethnic divides play a major role in many armed conflicts around the world and might serve as predetermined conflict lines following rapidly emerging societal tensions arising from disruptive events like natural disasters. We find evidence in global datasets that risk of armed-conflict outbreak is enhanced by climate-related disaster occurrence in ethnically fractionalized countries. Although we find no indications that environmental disasters directly trigger armed conflicts, our results imply that disasters might act as a threat multiplier in several of the world’s most conflict-prone regions. Social and political tensions keep on fueling armed conflicts around the world. Although each conflict is the result of an individual context-specific mixture of interconnected factors, ethnicity appears to play a prominent and almost ubiquitous role in many of them. This overall state of affairs is likely to be exacerbated by anthropogenic climate change and in particular climate-related natural disasters. Ethnic divides might serve as predetermined conflict lines in case of rapidly emerging societal tensions arising from disruptive events like natural disasters. Here, we hypothesize that climate-related disaster occurrence enhances armed-conflict outbreak risk in ethnically fractionalized countries. Using event coincidence analysis, we test this hypothesis based on data on armed-conflict outbreaks and climate-related natural disasters for the period 1980–2010. Globally, we find a coincidence rate of 9% regarding armed-conflict outbreak and disaster occurrence such as heat waves or droughts. Our analysis also reveals that, during the period in question, about 23% of conflict outbreaks in ethnically highly fractionalized countries robustly coincide with climatic calamities. Although we do not report evidence that climate-related disasters act as direct triggers of armed conflicts, the disruptive nature of these events seems to play out in ethnically fractionalized societies in a particularly tragic way. This observation has important implications for future security policies as several of the world’s most conflict-prone regions, including North and Central Africa as well as Central Asia, are both exceptionally vulnerable to anthropogenic climate change and characterized by deep ethnic divides.

Urban road networks — spatial networks with universal geometric features?

Abstract Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for the time evolution of urban road networks.

Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic windows can be easily made based on the maximum Lyapunov exponent of the system, this remains a challenging task for continuous systems, especially if only short time series are available (e.g., in case of experimental data). In this work, we demonstrate that nonlinear measures based on recurrence plots obtained from such trajectories provide a practicable alternative for numerically detecting shrimps. Traditional diagonal line-based measures of recurrence quantification analysis as well as measures from complex network theory are shown to allow an excellent classification of periodic and chaotic behavior in parameter space. Using the well-studied Rössler system as a benchmark example, we find that the average path length and the clustering coefficient of the resulting recurrence networks are particularly powerful discriminatory statistics for the identification of complex periodic windows.

Geometric detection of coupling directions by means of inter-system recurrence networks

Abstract We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled Rossler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying K > 2 coupled subsystems.