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- ItemTopology of sustainable management of dynamical systems with desirable states: From defining planetary boundaries to safe operating spaces in the Earth system(München : European Geopyhsical Union, 2016) Heitzig, J.; Kittel, T.; Donges, J.F.; Molkenthin, N.To keep the Earth system in a desirable region of its state space, such as defined by the recently suggested "tolerable environment and development window", "guardrails", "planetary boundaries", or "safe (and just) operating space for humanity", one needs to understand not only the quantitative internal dynamics of the system and the available options for influencing it (management) but also the structure of the system's state space with regard to certain qualitative differences. Important questions are, which state space regions can be reached from which others with or without leaving the desirable region, which regions are in a variety of senses "safe" to stay in when management options might break away, and which qualitative decision problems may occur as a consequence of this topological structure? In this article, we develop a mathematical theory of the qualitative topology of the state space of a dynamical system with management options and desirable states, as a complement to the existing literature on optimal control which is more focussed on quantitative optimization and is much applied in both the engineering and the integrated assessment literature. We suggest a certain terminology for the various resulting regions of the state space and perform a detailed formal classification of the possible states with respect to the possibility of avoiding or leaving the undesired region. Our results indicate that, before performing some form of quantitative optimization such as of indicators of human well-being for achieving certain sustainable development goals, a sustainable and resilient management of the Earth system may require decisions of a more discrete type that come in the form of several dilemmas, e.g. choosing between eventual safety and uninterrupted desirability, or between uninterrupted safety and larger flexibility. We illustrate the concepts and dilemmas drawing on conceptual models from climate science, ecology, coevolutionary Earth system modelling, economics, and classical mechanics, and discuss their potential relevance for the climate and sustainability debate, in particular suggesting several levels of planetary boundaries of qualitatively increasing safety.
- ItemRecurrence networks-a novel paradigm for nonlinear time series analysis(College Park, MD : Institute of Physics Publishing, 2010) Donner, R.V.; Zou, Y.; Donges, J.F.; Marwan, N.; Kurths, J.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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemTopology identification of complex network via chaotic ant swarm algorithm(New York, NY : Hindawi Publishing Corporation, 2013) Peng, H.; Li, L.; Kurths, J.; Li, S.; Yang, Y.Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.
- ItemTopology of products similarity network for market forecasting([Cham] : Springer International Publishing, 2019) Fan, Jingfang; Cohen, Keren; Shekhtman, Louis M.; Liu, Sibo; Meng, Jun; Louzoun, Yoram; Havlin, ShlomoThe detection and prediction of risk in financial markets is one of the main challenges of economic forecasting, and draws much attention from the scientific community. An even more challenging task is the prediction of the future relative gain of companies. We here develop a novel combination of product text analysis, network theory and topological based machine learning to study the future performance of companies in financial markets. Our network links are based on the similarity of firms’ products and constructed using the Securities Exchange Commission (SEC) filings of US listed firms. We find that several topological features of this network can serve as good precursors of risks or future gain of companies. We then apply machine learning to network attributes vectors for each node to predict successful and failing firms. The resulting accuracies are much better than current state of the art techniques. The framework presented here not only facilitates the prediction of financial markets but also provides insight and demonstrates the power of combining network theory and topology based machine learning.
- ItemGeneral scaling of maximum degree of synchronization in noisy complex networks(Bristol : Institute of Physics Publishing, 2014) Traxl, D.; Boers, N.; Kurths, J.The effects of white noise and global coupling strength on the maximum degree of synchronization in complex networks are explored. We perform numerical simulations of generic oscillator models with both linear and non-linear coupling functions on a broad spectrum of network topologies. The oscillator models include the Fitzhugh-Nagumo model, the Izhikevich model and the Kuramoto phase oscillator model. The network topologies range from regular, random and highly modular networks to scale-free and small-world networks, with both directed and undirected edges. We then study the dependency of the maximum degree of synchronization on the global coupling strength and the noise intensity. We find a general scaling of the synchronizability, and quantify its validity by fitting a regression model to the numerical data.
- ItemDetours around basin stability in power networks(Bristol : Institute of Physics Publishing, 2014) Schultz, P.; Heitzig, J.; Kurths, J.To analyse the relationship between stability against large perturbations and topological properties of a power transmission grid, we employ a statistical analysis of a large ensemble of synthetic power grids, looking for significant statistical relationships between the single-node basin stability measure and classical as well as tailormade weighted network characteristics. This method enables us to predict poor values of single-node basin stability for a large extent of the nodes, offering a node-wise stability estimation at low computational cost. Further, we analyse the particular function of certain network motifs to promote or degrade the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design.
- ItemIndividual nodes contribution to the mesoscale of complex networks(Bristol : Institute of Physics Publishing, 2014) Klimm, F.; Borge-Holthoefer, J.; Wessel, N.; Kurths, J.; Zamora-Lopez, G.The analysis of complex networks is devoted to the statistical characterization of the topology of graphs at different scales of organization in order to understand their functionality. While the modular structure of networks has become an essential element to better apprehend their complexity, the efforts to characterize the mesoscale of networks have focused on the identification of the modules rather than describing the mesoscale in an informative manner. Here we propose a framework to characterize the position every node takes within the modular configuration of complex networks and to evaluate their function accordingly. For illustration, we apply this framework to a set of synthetic networks, empirical neural networks, and to the transcriptional regulatory network of the Mycobacterium tuberculosis. We find that the architecture of both neuronal and transcriptional networks are optimized for the processing of multisensory information with the coexistence of well-defined modules of specialized components and the presence of hubs conveying information from and to the distinct functional domains.
- ItemRecovery time after localized perturbations in complex dynamical networks(Bristol : Institute of Physics Publishing, 2017) Mitra, C.; Kittel, T.; Choudhary, A.; Kurths, J.; Donner, R.V.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 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 slow nodes of the network from the relatively 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 global relaxation time when starting all the nodes from random initial conditions. Earlier work on relaxation time generally focused on investigating its dependence on macroscopic topological properties of the respective network. However, 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.
- ItemCharacterizing time series: When Granger causality triggers complex networks(Bristol : Institute of Physics Publishing, 2012) Ge, T.; Cui, Y.; Lin, W.; Kurths, J.; Liu, C.In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIH 7 human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length.
- ItemScaling Laws of Collective Ride-Sharing Dynamics(College Park, Md. : APS, 2020) Molkenthin, Nora; Schröder, Malte; Timme, MarcRide-sharing services may substantially contribute to future sustainable mobility. Their collective dynamics intricately depend on the topology of the underlying street network, the spatiotemporal demand distribution, and the dispatching algorithm. The efficiency of ride-sharing fleets is thus hard to quantify and compare in a unified way. Here, we derive an efficiency observable from the collective nonlinear dynamics and show that it exhibits a universal scaling law. For any given dispatcher, we find a common scaling that yields data collapse across qualitatively different topologies of model networks and empirical street networks from cities, islands, and rural areas. A mean-field analysis confirms this view and reveals a single scaling parameter that jointly captures the influence of network topology and demand distribution. These results further our conceptual understanding of the collective dynamics of ride-sharing fleets and support the evaluation of ride-sharing services and their transfer to previously unserviced regions or unprecedented demand patterns.