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- ItemExplosive death induced by mean–field diffusion in identical oscillators([London] : Macmillan Publishers Limited, part of Springer Nature, 2017) Verma, Umesh Kumar; Sharma, Amit; Kamal, Neeraj Kumar; Kurths, Jürgen; Shrimali, Manish DevWe report the occurrence of an explosive death transition for the first time in an ensemble of identical limit cycle and chaotic oscillators coupled via mean–field diffusion. In both systems, the variation of the normalized amplitude with the coupling strength exhibits an abrupt and irreversible transition to death state from an oscillatory state and this first order phase transition to death state is independent of the size of the system. This transition is quite general and has been found in all the coupled systems where in–phase oscillations co–exist with a coupling dependent homogeneous steady state. The backward transition point for this phase transition has been calculated using linear stability analysis which is in complete agreement with the numerics.
- ItemEpidemics with mutating infectivity on small-world networks([London] : Macmillan Publishers Limited, part of Springer Nature, 2020) Rüdiger, Sten; Plietzsch, Anton; Sagués, Francesc; Sokolov, Igor M.; Kurths, JürgenEpidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent’s infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation. © 2020, The Author(s).
- ItemNetwork-based identification and characterization of teleconnections on different scales([London] : Macmillan Publishers Limited, part of Springer Nature, 2019) Agarwal, Ankit; Caesar, Levke; Marwan, Norbert; Maheswaran, Rathinasamy; Merz, Bruno; Kurths, JürgenSea surface temperature (SST) patterns can – as surface climate forcing – affect weather and climate at large distances. One example is El Niño-Southern Oscillation (ENSO) that causes climate anomalies around the globe via teleconnections. Although several studies identified and characterized these teleconnections, our understanding of climate processes remains incomplete, since interactions and feedbacks are typically exhibited at unique or multiple temporal and spatial scales. This study characterizes the interactions between the cells of a global SST data set at different temporal and spatial scales using climate networks. These networks are constructed using wavelet multi-scale correlation that investigate the correlation between the SST time series at a range of scales allowing instantaneously deeper insights into the correlation patterns compared to traditional methods like empirical orthogonal functions or classical correlation analysis. This allows us to identify and visualise regions of – at a certain timescale – similarly evolving SSTs and distinguish them from those with long-range teleconnections to other ocean regions. Our findings re-confirm accepted knowledge about known highly linked SST patterns like ENSO and the Pacific Decadal Oscillation, but also suggest new insights into the characteristics and origins of long-range teleconnections like the connection between ENSO and Indian Ocean Dipole.
- ItemOverview of compressed sensing: Sensing model, reconstruction algorithm, and its applications(Basel : MDPI, 2020) Li, Lixiang; Fang, Yuan; Liu, Liwei; Peng, Haipeng; Kurths, Jürgen; Yang, YixianWith the development of intelligent networks such as the Internet of Things, network scales are becoming increasingly larger, and network environments increasingly complex, which brings a great challenge to network communication. The issues of energy-saving, transmission efficiency, and security were gradually highlighted. Compressed sensing (CS) helps to simultaneously solve those three problems in the communication of intelligent networks. In CS, fewer samples are required to reconstruct sparse or compressible signals, which breaks the restrict condition of a traditional Nyquist-Shannon sampling theorem. Here, we give an overview of recent CS studies, along the issues of sensing models, reconstruction algorithms, and their applications. First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing. We also present several state-of-the-art reconstruction algorithms of CS, including the convex optimization, greedy, and Bayesian algorithms. Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks. We discuss works related to CS technology and some CS essentials. © 2020 by the authors.
- ItemDynamic Network Characteristics of Power-electronics-based Power Systems([London] : Macmillan Publishers Limited, part of Springer Nature, 2020) Ji, Yuxi; He, Wei; Cheng, Shijie; Kurths, Jürgen; Zhan, MengPower flow studies in traditional power systems aim to uncover the stationary relationship between voltage amplitude and phase and active and reactive powers; they are important for both stationary and dynamic power system analysis. With the increasing penetration of large-scale power electronics devices including renewable generations interfaced with converters, the power systems become gradually power-electronics-dominant and correspondingly their dynamical behavior changes substantially. Due to the fast dynamics of converters, such as AC current controller, the quasi-stationary state approximation, which has been widely used in power systems, is no longer appropriate and should be reexamined. In this paper, for a better description of network characteristics, we develop a novel concept of dynamic power flow and uncover an explicit dynamic relation between the instantaneous powers and the voltage vectors. This mathematical relation has been well verified by simulations on transient analysis of a small power-electronics-based power system, and a small-signal frequency-domain stability analysis of a voltage source converter connected to an infinitely strong bus. These results demonstrate the applicability of the proposed method and shed an improved light on our understanding of power-electronics-dominant power systems, whose dynamical nature remains obscure.
- ItemData-Driven Discovery of Stochastic Differential Equations(Beijing : Engineering Sciences Press, 2022) Wang, Yasen; Fang, Huazhen; Jin, Junyang; Ma, Guijun; He, Xin; Dai, Xing; Yue, Zuogong; Cheng, Cheng; Zhang, Hai-Tao; Pu, Donglin; Wu, Dongrui; Yuan, Ye; Gonçalves, Jorge; Kurths, Jürgen; Ding, HanStochastic differential equations (SDEs) are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different sources. The identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system's dynamics. The practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data resources. This study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning (SBL) technique to search for a parsimonious, yet physically necessary representation from the space of candidate basis functions. More importantly, we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series data. The effectiveness of the proposed framework is demonstrated using real data on stock and oil prices, bearing variation, and wind speed, as well as simulated data on well-known stochastic dynamical systems, including the generalized Wiener process and Langevin equation. This framework aims to assist specialists in extracting stochastic mathematical models from random phenomena in the natural sciences, economics, and engineering fields for analysis, prediction, and decision making.
- ItemUniversality in spectral condensation([London] : Macmillan Publishers Limited, part of Springer Nature, 2020) Pavithran, Induja; Unni, Vishnu R.; Varghese, Alan J.; Premraj, D.; Sujith, R. I.; Vijayan, C.; Saha, Abhishek; Marwan, Norbert; Kurths, JürgenSelf-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.
- ItemStatistical Properties and Predictability of Extreme Epileptic Events([London] : Macmillan Publishers Limited, part of Springer Nature, 2019) Frolov, Nikita S.; Grubov, Vadim V.; Maksimenko, Vladimir A.; Lüttjohann, Annika; Makarov, Vladimir V.; Pavlov, Alexey N.; Sitnikova, Evgenia; Pisarchik, Alexander N.; Kurths, Jürgen; Hramov, Alexander E.The use of extreme events theory for the analysis of spontaneous epileptic brain activity is a relevant multidisciplinary problem. It allows deeper understanding of pathological brain functioning and unraveling mechanisms underlying the epileptic seizure emergence along with its predictability. The latter is a desired goal in epileptology which might open the way for new therapies to control and prevent epileptic attacks. With this goal in mind, we applied the extreme event theory for studying statistical properties of electroencephalographic (EEG) recordings of WAG/Rij rats with genetic predisposition to absence epilepsy. Our approach allowed us to reveal extreme events inherent in this pathological spiking activity, highly pronounced in a particular frequency range. The return interval analysis showed that the epileptic seizures exhibit a highly-structural behavior during the active phase of the spiking activity. Obtained results evidenced a possibility for early (up to 7 s) prediction of epileptic seizures based on consideration of EEG statistical properties.