@article{OzturkMarwanKorupetal.2018, author = {Ozturk, Ugur and Marwan, Norbert and Korup, Oliver and Saito, H. and Agarwa, Ankit and Grossman, M. J. and Zaiki, M. and Kurths, J{\"u}rgen}, title = {Complex networks for tracking extreme rainfall during typhoons}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {7}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5004480}, pages = {8}, year = {2018}, abstract = {Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons but mask out contributions of local convective storms. We propose a radial rank method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July.}, language = {en} } @article{BoccalettiHwangChavezetal.2006, author = {Boccaletti, Stefano and Hwang, Dong-Uk and Chavez, Mario and Amann, Andreas and Kurths, J{\"u}rgen and Pecora, Louis M.}, title = {Synchronization in dynamical networks : evolution along commutative graphs}, issn = {1539-3755}, doi = {10.1103/Physreve.74.016102}, year = {2006}, abstract = {Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior}, language = {en} } @article{VianaGrebogiPintoetal.2005, author = {Viana, R. L. and Grebogi, Celso and Pinto, S. E. D. and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen}, title = {Bubbling bifurcation : loss of synchronization and shadowing breakdown in complex systems}, year = {2005}, abstract = {Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved}, language = {en} } @article{LindTitzKuhlbrodtetal.2004, author = {Lind, P. G. and Titz, Sven Holger and Kuhlbrodt, Till and Corte-Real, J. A. M. and Kurths, J{\"u}rgen and Gallas, J. A. C. and Feudel, Ulla}, title = {Coupled bistable maps : a tool to study convection parameterization in ocean models}, issn = {0218-1274}, year = {2004}, abstract = {We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells. For large diffusion our model exhibits a phase transition from convective patterns to a homogeneous state over the entire lattice. In hysteresis experiments we find staircase behavior depending on stability thresholds of local convection patterns. This nonphysical behavior is suspected to induce spurious abrupt changes in the spreading of convection in ocean models. The final steady state of convective cells depends not only on the magnitude of the advective velocity but also on its direction, implying a possible bias in the development of convective patterns. Such bias points to the need for an appropriate choice of grid geometry in ocean modeling}, language = {en} } @article{DeShazerTigheKurthsetal.2004, author = {DeShazer, D. J. and Tighe, B. P. and Kurths, M. and Roy, R.}, title = {Experimental observation of noise-induced synchronization of bursting dynamical systems}, issn = {1077-260X}, year = {2004}, abstract = {Can bursts in dynamical systems be synchronized by a weak, common, noise background? We observe large, uncorrelated bursts of intensity fluctuations in two almost identical erbium-doped fiber ring lasers, initiated by common injection of a weak, constant intensity optical signal. Significant synchronization of the bursts is obtained for noise and sinusoidal modulation of the injected light intensity. Measurements of the burst statistics and synchronization are presented}, language = {en} } @article{ThielRomanoSchwarzetal.2004, author = {Thiel, M. and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Timmer, Jens}, title = {Surrogate-based hypothesis test without surrogates}, issn = {0218-1274}, year = {2004}, abstract = {Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1}, language = {en} } @article{ThielRomanoKurths2004, author = {Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen}, title = {How much information is contained in a recurrence plot?}, issn = {0375-9601}, year = {2004}, abstract = {Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved}, language = {en} } @article{ThielRomanoReadetal.2004, author = {Thiel, M. and Romano, Maria Carmen and Read, P. L. and Kurths, J{\"u}rgen}, title = {Estimation of dynamical invariants without embedding by recurrence plots}, issn = {1054-1500}, year = {2004}, abstract = {In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics}, language = {en} } @article{VianaGrebogiPintoetal.2003, author = {Viana, R. L. and Grebogi, Celso and Pinto, Seds and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen}, title = {Validity of numerical trajectories in the synchronization transition of complex systems}, issn = {1063-651X}, year = {2003}, abstract = {We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties}, language = {en} } @article{FlorenceDahlemAlmeidaetal.2009, author = {Florence, Gerson and Dahlem, Markus A. and Almeida, Ant{\^o}nio-Carlos G. and Bassani, Jos{\´e} W. M. and Kurths, J{\"u}rgen}, title = {The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study}, issn = {0022-5193}, doi = {10.1016/j.jtbi.2009.01.032}, year = {2009}, abstract = {Experimental evidences point Out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular tons) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K+](o) and a decrease of extracellular calcium concentration [Ca2+](o) which raises the neuronal excitability. However, whether the high [K+](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K+](o) and zero [Ca2+](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na+-K+ pump, ion diffusion and glial buffering. Within these Conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na+- K+ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K+ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K+](o), transiting to an elevated state of neuronal excitability. Effects of high [K+](o), are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K+](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K+](o) by outward K+ flow depresses K+ Currents in a positive feedback way. At the last stage, due to the depression of K+ currents, the Na+-K+ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K+](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.}, language = {en} } @article{GozolchianiMoshelHausdorffetal.2006, author = {Gozolchiani, Avi and Moshel, Shay and Hausdorff, Jeffrey M. and Simon, Ely and Kurths, J{\"u}rgen and Havlin, Shlomo}, title = {Decaying of phase synchronization in parkinsonian tremor}, issn = {0378-4371}, doi = {10.1016/j.physa.2005.10.033}, year = {2006}, abstract = {We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.}, language = {en} } @article{BergnerFrascaSciutoetal.2012, author = {Bergner, Andre and Frasca, M. and Sciuto, G. and Buscarino, A. and Ngamga, Eulalie Joelle and Fortuna, L. and Kurths, J{\"u}rgen}, title = {Remote synchronization in star networks}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {85}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.85.026208}, pages = {7}, year = {2012}, abstract = {We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.}, language = {en} } @article{SrinivasanSenthilkumarMohamedetal.2012, author = {Srinivasan, K. and Senthilkumar, D. V. and Mohamed, I. Raja and Murali, K. and Lakshmanan, M. and Kurths, J{\"u}rgen}, title = {Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua's circuits without delay}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {22}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {2}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4711375}, pages = {8}, year = {2012}, abstract = {We construct a new RC phase shift network based Chua's circuit, which exhibits a period-doubling bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chua's oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS or CS is demonstrated without using a variable delay line both experimentally and numerically.}, language = {en} } @article{GoswamiShekatkarRheinwaltetal.2015, author = {Goswami, Bedartha and Shekatkar, Snehal M. and Rheinwalt, Aljoscha and Ambika, G. and Kurths, J{\"u}rgen}, title = {A random interacting network model for complex networks}, series = {Scientific reports}, volume = {5}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/srep18183}, pages = {10}, year = {2015}, abstract = {We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.}, language = {en} } @article{GandhimathiRajasekarKurths2006, author = {Gandhimathi, V. M. and Rajasekar, S. and Kurths, J{\"u}rgen}, title = {Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators}, series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, volume = {360}, journal = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, number = {2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0375-9601}, doi = {10.1016/j.physleta.2006.08.051}, pages = {279 -- 286}, year = {2006}, abstract = {We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved.}, language = {en} } @article{ZouThielRomanoetal.2006, author = {Zou, Yong and Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen and Bi, Q.}, title = {Shrimp structure and associated dynamics in parametrically excited oscillators}, series = {International journal of bifurcation and chaos : in applied sciences and engineering}, volume = {16}, journal = {International journal of bifurcation and chaos : in applied sciences and engineering}, number = {12}, publisher = {World Scientific Publ. Co}, address = {Singapore}, issn = {0218-1274}, doi = {10.1142/S0218127406016987}, pages = {3567 -- 3579}, year = {2006}, abstract = {We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.}, language = {en} } @article{RomanoThielSchwarzetal.2001, author = {Romano, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Lange, Holger and Hauhs, M.}, title = {Conceptual model of runoff from a forested catchment}, year = {2001}, abstract = {We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data.}, language = {en} } @article{HassanKurths2001, author = {Hassan, M. K. and Kurths, J{\"u}rgen}, title = {Transition from random to ordered fractals in fragmentation of particles in an open system}, year = {2001}, language = {en} } @article{HassanKurths2001, author = {Hassan, M. K. and Kurths, J{\"u}rgen}, title = {Competitive random sequential adsorption of point and fixed-sized particles: analytical results}, year = {2001}, language = {en} } @article{RomanoThielKurthsetal.2005, author = {Romano, Maria Carmen and Thiel, M. and Kurths, J{\"u}rgen and Kiss, Istvan Z. and Hudson, J. L.}, title = {Detection of synchronization for non-phase-coherent and non-stationary data}, issn = {0295-5075}, year = {2005}, abstract = {We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rossler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase- coherent and even non-stationary time series}, language = {en} } @article{RamosBuilesJaramilloPovedaetal.2017, author = {Ramos, Antonio M. T. and Builes-Jaramillo, Alejandro and Poveda, German and Goswami, Bedartha and Macau, Elbert E. N. and Kurths, J{\"u}rgen and Marwan, Norbert}, title = {Recurrence measure of conditional dependence and applications}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {95}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.95.052206}, pages = {8}, year = {2017}, abstract = {Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.}, language = {en} } @article{BreitenbachRehfeldGoswamietal.2012, author = {Breitenbach, Sebastian Franz Martin and Rehfeld, Kira and Goswami, Bedartha and Baldini, James U. L. and Ridley, H. E. and Kennett, D. J. and Prufer, K. M. and Aquino, Valorie V. and Asmerom, Yemane and Polyak, V. J. and Cheng, Hai and Kurths, J{\"u}rgen and Marwan, Norbert}, title = {Constructing Proxy Records from Age models (COPRA)}, series = {Climate of the past : an interactive open access journal of the European Geosciences Union}, volume = {8}, journal = {Climate of the past : an interactive open access journal of the European Geosciences Union}, number = {5}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1814-9324}, doi = {10.5194/cp-8-1765-2012}, pages = {1765 -- 1779}, year = {2012}, abstract = {Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question. We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage.}, language = {en} } @article{BoersBarbosaBookhagenetal.2015, author = {Boers, Niklas and Barbosa, Henrique M. J. and Bookhagen, Bodo and Marengo, Jose A. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Propagation of Strong Rainfall Events from Southeastern South America to the Central Andes}, series = {Journal of climate}, volume = {28}, journal = {Journal of climate}, number = {19}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0894-8755}, doi = {10.1175/JCLI-D-15-0137.1}, pages = {7641 -- 7658}, year = {2015}, abstract = {Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70\% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes.}, language = {en} }