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- ItemDynamical phenomena in complex networks: fundamentals and applications(Berlin ; Heidelberg : Springer, 2021) Yanchuk, Serhiy; Roque, Antonio C.; Macau, Elbert E. N.; Kurths, JürgenThis special issue presents a series of 33 contributions in the area of dynamical networks and their applications. Part of the contributions is devoted to theoretical and methodological aspects of dynamical networks, such as collective dynamics of excitable systems, spreading processes, coarsening, synchronization, delayed interactions, and others. A particular focus is placed on applications to neuroscience and Earth science, especially functional climate networks. Among the highlights, various methods for dealing with noise and stochastic processes in neuroscience are presented. A method for constructing weighted networks with arbitrary topologies from a single dynamical node with delayed feedback is introduced. Also, a generalization of the concept of geodesic distances, a path-integral formulation of network-based measures is developed, which provides fundamental insights into the dynamics of disease transmission. The contributions from the Earth science application field substantiate predictive power of climate networks to study challenging Earth processes and phenomena.
- ItemA recurrent plot based stochastic nonlinear ray propagation model for underwater signal propagation([London] : IOP, 2020) Haiyang, Yao; Haiyan, Wang; Yong, Xu; Kurths, JuergenA stochastic nonlinear ray propagation model is proposed to carry out an exploration of the nonlinear ray theory in underwater signal propagation. The recurrence plot method is proposed to quantify the ray chaos and stochastics to optimize the model. Based on this method, the distribution function of the control parameter d is derived. Experiments and simulations indicate that this stochastic nonlinear ray propagation model provides a good explanation and description on the stochastic frequency shift in underwater signal propagation. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
- ItemSpecial Issue “Trends in recurrence analysis of dynamical systems”(Berlin ; Heidelberg : Springer, 2023) Marwan, Norbert; Webber, Charles L.; Rysak, Andrzej[No abstract available]
- ItemCoupled network analysis revealing global monthly scale co-variability patterns between sea-surface temperatures and precipitation in dependence on the ENSO state(Berlin ; Heidelberg : Springer, 2021) Ekhtiari, Nikoo; Ciemer, Catrin; Kirsch, Catrin; Donner, Reik V.The Earth’s climate is a complex system characterized by multi-scale nonlinear interrelationships between different subsystems like atmosphere and ocean. Among others, the mutual interdependence between sea surface temperatures (SST) and precipitation (PCP) has important implications for ecosystems and societies in vast parts of the globe but is still far from being completely understood. In this context, the globally most relevant coupled ocean–atmosphere phenomenon is the El Niño–Southern Oscillation (ENSO), which strongly affects large-scale SST variability as well as PCP patterns all around the globe. Although significant achievements have been made to foster our understanding of ENSO’s global teleconnections and climate impacts, there are many processes associated with ocean–atmosphere interactions in the tropics and extratropics, as well as remote effects of SST changes on PCP patterns that have not yet been unveiled or fully understood. In this work, we employ coupled climate network analysis for characterizing dominating global co-variability patterns between SST and PCP at monthly timescales. Our analysis uncovers characteristic seasonal patterns associated with both local and remote statistical linkages and demonstrates their dependence on the type of the current ENSO phase (El Niño, La Niña or neutral phase). Thereby, our results allow identifying local interactions as well as teleconnections between SST variations and global precipitation patterns.
- ItemNeural partial differential equations for chaotic systems([London] : IOP, 2021) Gelbrecht, Maximilian; Boers, Niklas; Kurths, JürgenWhen predicting complex systems one typically relies on differential equation which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. We show that this can be used to predict paradigmatic, high-dimensional chaotic partial differential equations even when only short and incomplete datasets are available. The forecast horizon for these high dimensional systems is about an order of magnitude larger than the length of the training data.
- ItemEvolving climate network perspectives on global surface air temperature effects of ENSO and strong volcanic eruptions(Berlin ; Heidelberg : Springer, 2021) Kittel, Tim; Ciemer, Catrin; Lotfi, Nastaran; Peron, Thomas; Rodrigues, Francisco; Kurths, Jürgen; Donner, Reik V.Episodically occurring internal (climatic) and external (non-climatic) disruptions of normal climate variability are known to both affect spatio-temporal patterns of global surface air temperatures (SAT) at time-scales between multiple weeks and several years. The magnitude and spatial manifestation of the corresponding effects depend strongly on the specific type of perturbation and may range from weak spatially coherent yet regionally confined trends to a global reorganization of co-variability due to the excitation or inhibition of certain large-scale teleconnectivity patterns. Here, we employ functional climate network analysis to distinguish qualitatively the global climate responses to different phases of the El Niño–Southern Oscillation (ENSO) from those to the three largest volcanic eruptions since the mid-20th century as the two most prominent types of recurrent climate disruptions. Our results confirm that strong ENSO episodes can cause a temporary breakdown of the normal hierarchical organization of the global SAT field, which is characterized by the simultaneous emergence of consistent regional temperature trends and strong teleconnections. By contrast, the most recent strong volcanic eruptions exhibited primarily regional effects rather than triggering additional long-range teleconnections that would not have been present otherwise. By relying on several complementary network characteristics, our results contribute to a better understanding of climate network properties by differentiating between climate variability reorganization mechanisms associated with internal variability versus such triggered by non-climatic abrupt and localized perturbations.
- ItemDynamical network size estimation from local observations([London] : IOP, 2020) Tang, Xiuchuan; Huo, Wei; Yuan, Ye; Li, Xiuting; Shi, Ling; Kurths, JürgenHere we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
- ItemEstimating global mean sea-level rise and its uncertainties by 2100 and 2300 from an expert survey(London : Springer Nature, 2020) Horton, Benjamin P.; Khan, Nicole S.; Cahill, Niamh; Lee, Janice S. H.; Shaw, Timothy A.; Garner, Andra J.; Kemp, Andrew C.; Engelhart, Simon E.; Rahmstorf, StefanSea-level rise projections and knowledge of their uncertainties are vital to make informed mitigation and adaptation decisions. To elicit projections from members of the scientific community regarding future global mean sea-level (GMSL) rise, we repeated a survey originally conducted five years ago. Under Representative Concentration Pathway (RCP) 2.6, 106 experts projected a likely (central 66% probability) GMSL rise of 0.30–0.65 m by 2100, and 0.54–2.15 m by 2300, relative to 1986–2005. Under RCP 8.5, the same experts projected a likely GMSL rise of 0.63–1.32 m by 2100, and 1.67–5.61 m by 2300. Expert projections for 2100 are similar to those from the original survey, although the projection for 2300 has extended tails and is higher than the original survey. Experts give a likelihood of 42% (original survey) and 45% (current survey) that under the high-emissions scenario GMSL rise will exceed the upper bound (0.98 m) of the likely range estimated by the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, which is considered to have an exceedance likelihood of 17%. Responses to open-ended questions suggest that the increases in upper-end estimates and uncertainties arose from recent influential studies about the impact of marine ice cliff instability on the meltwater contribution to GMSL rise from the Antarctic Ice Sheet. © 2020, The Author(s).
- ItemExtending Transition Path Theory: Periodically Driven and Finite-Time Dynamics(New York, NY : Springer, 2020) Helfmann, Luzie; Ribera Borrell, Enric; Schütte, Christof; Koltai, PéterGiven two distinct subsets A, B in the state space of some dynamical system, transition path theory (TPT) was successfully used to describe the statistical behavior of transitions from A to B in the ergodic limit of the stationary system. We derive generalizations of TPT that remove the requirements of stationarity and of the ergodic limit and provide this powerful tool for the analysis of other dynamical scenarios: periodically forced dynamics and time-dependent finite-time systems. This is partially motivated by studying applications such as climate, ocean, and social dynamics. On simple model examples, we show how the new tools are able to deliver quantitative understanding about the statistical behavior of such systems. We also point out explicit cases where the more general dynamical regimes show different behaviors to their stationary counterparts, linking these tools directly to bifurcations in non-deterministic systems. © 2020, The Author(s).
- ItemReconstructing complex system dynamics from time series: a method comparison([London] : IOP, 2020) Hassanibesheli, Forough; Boers, Niklas; Kurths, JürgenModeling complex systems with large numbers of degrees of freedom has become a grand challenge over the past decades. In many situations, only a few variables are actually observed in terms of measured time series, while the majority of variables - which potentially interact with the observed ones - remain hidden. A typical approach is then to focus on the comparably few observed, macroscopic variables, assuming that they determine the key dynamics of the system, while the remaining ones are represented by noise. This naturally leads to an approximate, inverse modeling of such systems in terms of stochastic differential equations (SDEs), with great potential for applications from biology to finance and Earth system dynamics. A well-known approach to retrieve such SDEs from small sets of observed time series is to reconstruct the drift and diffusion terms of a Langevin equation from the data-derived Kramers-Moyal (KM) coefficients. For systems where interactions between the observed and the unobserved variables are crucial, the Mori-Zwanzig formalism (MZ) allows to derive generalized Langevin equations that contain non-Markovian terms representing these interactions. In a similar spirit, the empirical model reduction (EMR) approach has more recently been introduced. In this work we attempt to reconstruct the dynamical equations of motion of both synthetical and real-world processes, by comparing these three approaches in terms of their capability to reconstruct the dynamics and statistics of the underlying systems. Through rigorous investigation of several synthetical and real-world systems, we confirm that the performance of the three methods strongly depends on the intrinsic dynamics of the system at hand. For instance, statistical properties of systems exhibiting weak history-dependence but strong state-dependence of the noise forcing, can be approximated better by the KM method than by the MZ and EMR approaches. In such situations, the KM method is of a considerable advantage since it can directly approximate the state-dependent noise. However, limitations of the KM approximation arise in cases where non-Markovian effects are crucial in the dynamics of the system. In these situations, our numerical results indicate that methods that take into account interactions between observed and unobserved variables in terms of non-Markovian closure terms (i.e., the MZ and EMR approaches), perform comparatively better. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft