@article{SchwarzSpahnGrebogietal.1999,
  author    = {Schwarz, Udo and Spahn, Frank and Grebogi, Celso and Kurths, J{\"u}rgen and Petzschmann, Olaf},
  title     = {Length scales of clustering in granular gases},
  year      = {1999},
  language  = {en}
}
@misc{MotterMatiasKurthsetal.2006,
  author    = {Motter, Adilson E. and Matias, Manuel A. and Kurths, J{\"u}rgen and Ott, Edward},
  title     = {Dynamics on complex networks and applications},
  series = {Physica. D, Nonlinear phenomena},
  volume    = {224},
  journal   = {Physica. D, Nonlinear phenomena},
  number    = {1-2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.09.012},
  pages     = {VII -- VIII},
  year      = {2006},
  language  = {en}
}
@article{ZemanovaZhouKurths2006,
  author    = {Zemanova, Lucia and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Structural and functional clusters of complex brain networks},
  series = {Physica, D, Nonlinear phenomena},
  volume    = {224},
  journal   = {Physica, D, Nonlinear phenomena},
  number    = {1-2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.09.008},
  pages     = {202 -- 212},
  year      = {2006},
  abstract  = {Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.},
  language  = {en}
}
@article{MeucciSalvadoriIvanchenkoetal.2006,
  author    = {Meucci, Riccardo and Salvadori, Francesco and Ivanchenko, Mikhail V. and Al Naimee, Kais and Zhou, Chansong and Arecchi, Fortunato Tito and Boccaletti, Stefano and Kurths, J{\"u}rgen},
  title     = {Synchronization of spontaneous bursting in a CO2 laser},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {74},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.74.066207},
  pages     = {6},
  year      = {2006},
  abstract  = {We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.},
  language  = {en}
}
@unpublished{PikovskijZaksFeudeletal.1995,
  author    = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen},
  title     = {Singular continuous spectra in dissipative dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787},
  year      = {1995},
  abstract  = {We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.},
  language  = {en}
}
@article{RosenblumPikovskijKurths2004,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Synchronization approach to analysis of biological systems},
  issn      = {0219-4775},
  year      = {2004},
  abstract  = {In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach},
  language  = {en}
}
@article{RosenblumKurthsPikovskij2001,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij},
  title     = {Comment on "Phase synchronization in discrete chaotic systems"},
  year      = {2001},
  abstract  = {Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.},
  language  = {en}
}
@article{PopovychMaistrenkoMosekildeetal.2001,
  author    = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Transcritical riddling in a system of coupled maps},
  year      = {2001},
  abstract  = {The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.},
  language  = {en}
}
@article{PikovskijRosenblumKurths2000,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in regular and chaotic systems},
  issn      = {0218-1274},
  year      = {2000},
  language  = {en}
}
@book{PikovskijRosenblumKurths2001,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen},
  title     = {Synchronization : a universal concept in nonlinear sciences},
  series = {Cambridge nonlinear science series},
  volume    = {12},
  journal   = {Cambridge nonlinear science series},
  edition   = {1st paperback ed., repr},
  publisher = {Cambridge Univ. Press},
  address   = {Cambridge},
  isbn      = {0-521-59285-2},
  pages     = {XIX, 411 S. : Ill., graph. Darst.},
  year      = {2001},
  language  = {en}
}
@article{PikovskijRosenblumZaksetal.1999,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Zaks, Michael A. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of regular and chaotic oscillators},
  year      = {1999},
  language  = {en}
}
@article{PopovychMaistrenkoMosekildeetal.2000,
  author    = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Transcritical loss of synchronization in coupled chaotic systems},
  year      = {2000},
  language  = {en}
}
@article{ZaksPikovskijKurths1999,
  author    = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {On the generalized dimensions for the fourier spectrum of the thue-morse sequence},
  year      = {1999},
  language  = {en}
}
@article{TassRosenblumWeuleetal.1998,
  author    = {Tass, Peter and Rosenblum, Michael and Weule, J. and Kurths, J{\"u}rgen and Pikovskij, Arkadij and Volkmann, J. and Schnitzler, A. and Freund, H.-J.},
  title     = {Detection of n:m phase locking from noisy data : application to magnetoencephalography},
  year      = {1998},
  abstract  = {We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {From Phase to Lag Synchronization in Coupled Chaotic Oscillators},
  year      = {1997},
  abstract  = {We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.},
  language  = {en}
}
@article{PikovskijKurths1997,
  author    = {Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Coherence Resonance in a Noise-Driven Excitable System},
  year      = {1997},
  abstract  = {We study the dynamics of the excitable Fitz Hugh-Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon.},
  language  = {en}
}
@article{RosenblumKurthsPikovskijetal.1998,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij and Schafer, C. and Tass, Peter and Abel, Hans-Henning},
  title     = {Synchronization in Noisy Systems and Cardiorespiratory Interaction},
  year      = {1998},
  language  = {en}
}
@article{RuzickScheffczykPikovskijetal.1997,
  author    = {Ruzick, Oliver and Scheffczyk, Christian and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Dynamics of chaos-order interface in coupled map lattices},
  year      = {1997},
  language  = {en}
}
@article{ZaksPikovskijKurths1998,
  author    = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Symbolic dynamics behind the singular continuous power spectra of continuous flows},
  year      = {1998},
  language  = {en}
}
@article{WittKurthsPikovskij1998,
  author    = {Witt, Annette and Kurths, J{\"u}rgen and Pikovskij, Arkadij},
  title     = {Testing stationarity in time series},
  year      = {1998},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in noisy and chaotic oscillators},
  year      = {1997},
  language  = {en}
}
@article{ZaksPikovskijKurths1997,
  author    = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {On the correlation dimension of the spectral measure for the Thue-Morse sequence},
  year      = {1997},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in driven and coupled chaotic oscillators},
  year      = {1997},
  language  = {en}
}
@article{RosenblumPikovskijKurths1997,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Effect of phase synchronization in driven chaotic oscillators},
  year      = {1997},
  language  = {en}
}
@article{PikovskijKurths1997,
  author    = {Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Coherence resonance in a noise-driven excitable system},
  year      = {1997},
  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{ZhouKurthsKissetal.2002,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen and Kiss, Istvan Z. and Hudson, J. L.},
  title     = {Noise-enhanced phase synchronization of chaotic oscillators},
  year      = {2002},
  language  = {en}
}
@unpublished{KurthsPikovskijScheffczyk1994,
  author    = {Kurths, J{\"u}rgen and Pikovskij, Arkadij and Scheffczyk, Christian},
  title     = {Roughening interfaces in deterministic dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13447},
  year      = {1994},
  abstract  = {Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.},
  language  = {en}
}
@article{StolbovaSurovyatkinaBookhagenetal.2016,
  author    = {Stolbova, Veronika and Surovyatkina, Elena and Bookhagen, Bodo and Kurths, J{\"u}rgen},
  title     = {Tipping elements of the Indian monsoon: Prediction of onset and withdrawal},
  series = {Geophysical research letters},
  volume    = {43},
  journal   = {Geophysical research letters},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {0094-8276},
  doi       = {10.1002/2016GL068392},
  pages     = {3982 -- 3990},
  year      = {2016},
  abstract  = {Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation.},
  language  = {en}
}
@article{CiemerBoersHirotaetal.2019,
  author    = {Ciemer, Catrin and Boers, Niklas and Hirota, Marina and Kurths, J{\"u}rgen and M{\"u}ller-Hansen, Finn and Oliveira, Rafael S. and Winkelmann, Ricarda},
  title     = {Higher resilience to climatic disturbances in tropical vegetation exposed to more variable rainfall},
  series = {Nature geoscience},
  volume    = {12},
  journal   = {Nature geoscience},
  number    = {3},
  publisher = {Nature Publ. Group},
  address   = {New York},
  issn      = {1752-0894},
  doi       = {10.1038/s41561-019-0312-z},
  pages     = {174 -- 179},
  year      = {2019},
  abstract  = {With ongoing global warming, the amount and frequency of precipitation in the tropics is projected to change substantially. While it has been shown that tropical forests and savannahs are sustained within the same intermediate mean annual precipitation range, the mechanisms that lead to the resilience of these ecosystems are still not fully understood. In particular, the long-term impact of rainfall variability on resilience is as yet unclear. Here we present observational evidence that both tropical forest and savannah exposed to a higher rainfall variability-in particular on interannual scales-during their long-term past are overall more resilient against climatic disturbances. Based on precipitation and tree cover data in the Brazilian Amazon basin, we constructed potential landscapes that enable us to systematically measure the resilience of the different ecosystems. Additionally, we infer that shifts from forest to savannah due to decreasing precipitation in the future are more likely to occur in regions with a precursory lower rainfall variability. Long-term rainfall variability thus needs to be taken into account in resilience analyses and projections of vegetation response to climate change.},
  language  = {en}
}
@misc{CiemerRehmKurthsetal.2020,
  author    = {Ciemer, Catrin and Rehm, Lars and Kurths, J{\"u}rgen and Donner, Reik Volker and Winkelmann, Ricarda and Boers, Niklas},
  title     = {An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {9},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-52586},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-525863},
  pages     = {12},
  year      = {2020},
  abstract  = {Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.},
  language  = {en}
}
@article{CiemerRehmKurthsetal.2020,
  author    = {Ciemer, Catrin and Rehm, Lars and Kurths, J{\"u}rgen and Donner, Reik Volker and Winkelmann, Ricarda and Boers, Niklas},
  title     = {An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures},
  series = {Environmental Research Letters},
  volume    = {15},
  journal   = {Environmental Research Letters},
  number    = {9},
  publisher = {IOP - Institute of Physics Publishing},
  address   = {Bristol},
  pages     = {10},
  year      = {2020},
  abstract  = {Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.},
  language  = {en}
}
@misc{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin},
  title     = {Twin Surrogates to Test for Complex Synchronisation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57231},
  year      = {2006},
  abstract  = {We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems.},
  language  = {en}
}
@article{IvanchenkoOsipovShalfeevetal.2004,
  author    = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization in ensembles of bursting oscillators},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles},
  language  = {en}
}
@article{IvanchenkoOsipovShalfeevetal.2004,
  author    = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of chaotic intermittent oscillations},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization},
  language  = {en}
}
@article{OsipovPikovskijKurths2002,
  author    = {Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase Synchronization of Chaotic Rotators},
  year      = {2002},
  abstract  = {We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.},
  language  = {en}
}
@article{RosenblumPikovskijKurthsetal.2002,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen and Osipov, Grigory V. and Kiss, Istvan Z. and Hudson, J. L.},
  title     = {Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics},
  year      = {2002},
  language  = {en}
}
@article{ZaksRosenblumPikovskijetal.1997,
  author    = {Zaks, Michael A. and Rosenblum, Michael and Pikovskij, Arkadij and Osipov, Grigory V. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of chaotic oscillations in terms of periodic orbits},
  issn      = {1054-1500},
  year      = {1997},
  language  = {en}
}
@article{PikovskijRosenblumOsipovetal.1997,
  author    = {Pikovskij, Arkadij and Rosenblum, Michael and Osipov, Grigory V. and Kurths, J{\"u}rgen},
  title     = {Phase synchronization effects in a lattice of nonidentical R{\"o}ssler oscillators},
  year      = {1997},
  language  = {en}
}
@article{RosenblumOsipovPikovskijetal.1997,
  author    = {Rosenblum, Michael and Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Phase synchronization of chaotic oscillators by external driving},
  year      = {1997},
  language  = {en}
}
@article{BoccalettiKurthsOsipov2002,
  author    = {Boccaletti, Stefano and Kurths, J{\"u}rgen and Osipov, Grigory V.},
  title     = {The synchronization of chaotic systems},
  year      = {2002},
  language  = {en}
}
@article{OsipovKurths2002,
  author    = {Osipov, Grigory V. and Kurths, J{\"u}rgen},
  title     = {Regular and chaotic phase synchronization of coupled circle maps},
  year      = {2002},
  language  = {en}
}
@article{OsipovRosenblumPikovskijetal.1997,
  author    = {Osipov, Grigory V. and Rosenblum, Michael and Pikovskij, Arkadij and Zaks, Michael A. and Kurths, J{\"u}rgen},
  title     = {Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization},
  year      = {1997},
  abstract  = {The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.},
  language  = {en}
}
@article{IvanchenkoOsipovShalfeevetal.2004,
  author    = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen},
  title     = {Synchronization of two non-scalar-coupled limit-cycle oscillators},
  year      = {2004},
  abstract  = {Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{BelykhOsipovKucklaenderetal.2005,
  author    = {Belykh, Vladimir N. and Osipov, Grigory V. and Kuckl{\"a}nder, Nina and Blasius, Bernd and Kurths, J{\"u}rgen},
  title     = {Automatic control of phase synchronization in coupled complex oscillators},
  year      = {2005},
  abstract  = {We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.},
  language  = {en}
}
@article{KurthsRomanoThieletal.2006,
  author    = {Kurths, J{\"u}rgen and Romano, Maria Carmen and Thiel, Marco and Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kiss, Istvan Z. and Hudson, John L.},
  title     = {Synchronization analysis of coupled noncoherent oscillators},
  issn      = {0924-090X},
  doi       = {10.1007/s11071-006-1957-x},
  year      = {2006},
  abstract  = {We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators},
  language  = {en}
}
@article{OsipovIvanchenkoKurthsetal.2005,
  author    = {Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kurths, J{\"u}rgen and Hu, B.},
  title     = {Synchronized chaotic intermittent and spiking behavior in coupled map chains},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks},
  language  = {en}
}
@article{MaheswaranAgarwalSivakumaretal.2019,
  author    = {Maheswaran, Rathinasamy and Agarwal, Ankit and Sivakumar, Bellie and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Wavelet analysis of precipitation extremes over India and teleconnections to climate indices},
  series = {Stochastic Environmental Research and Risk Assessment},
  volume    = {33},
  journal   = {Stochastic Environmental Research and Risk Assessment},
  number    = {11-12},
  publisher = {Springer},
  address   = {New York},
  issn      = {1436-3240},
  doi       = {10.1007/s00477-019-01738-3},
  pages     = {2053 -- 2069},
  year      = {2019},
  abstract  = {Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Nino 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Nino 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region.},
  language  = {en}
}
@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{MarwanNowaczykKurthsetal.2001,
  author    = {Marwan, Norbert and Nowaczyk, Norbert R. and Kurths, J{\"u}rgen and Thiel, Marco},
  title     = {Cross recurrence plot based rescaling of geological time series},
  issn      = {1029-7006},
  year      = {2001},
  abstract  = {The rescaling of geological data series to a geological reference time series is of major interest in many investigations. For example, geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Usually this synchronization is performed visually and by hand. Instead of using this wiggle matching by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and rescaling of geological data to a given time scale is much easier and faster than by hand.},
  language  = {en}
}
@article{AgarwalMaheswaranMarwanetal.2018,
  author    = {Agarwal, Ankit and Maheswaran, Rathinasamy and Marwan, Norbert and Caesar, Levke and Kurths, J{\"u}rgen},
  title     = {Wavelet-based multiscale similarity measure for complex networks},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {91},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  number    = {11},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2018-90460-6},
  pages     = {12},
  year      = {2018},
  abstract  = {In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson's correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson's correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.},
  language  = {en}
}
@article{KurthsAgarwalShuklaetal.2019,
  author    = {Kurths, J{\"u}rgen and Agarwal, Ankit and Shukla, Roopam and Marwan, Norbert and Maheswaran, Rathinasamy and Caesar, Levke and Krishnan, Raghavan and Merz, Bruno},
  title     = {Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach},
  series = {Nonlinear processes in geophysics},
  volume    = {26},
  journal   = {Nonlinear processes in geophysics},
  number    = {3},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1023-5809},
  doi       = {10.5194/npg-26-251-2019},
  pages     = {251 -- 266},
  year      = {2019},
  abstract  = {A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Ni{\~n}o-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting.},
  language  = {en}
}
@article{MarwanKurths2001,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Nonlinear analysis of bivariate data with cross recurrence plots},
  year      = {2001},
  abstract  = {We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.},
  language  = {en}
}
@article{WesselMarwanMeyerfeldtetal.2001,
  author    = {Wessel, Niels and Marwan, Norbert and Meyerfeldt, Udo and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia},
  year      = {2001},
  abstract  = {Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the},
  language  = {en}
}
@article{MarwanSchwarzKurthsetal.2000,
  author    = {Marwan, Norbert and Schwarz, Udo and Kurths, J{\"u}rgen and Strecker, Manfred},
  title     = {ENSO Impact on landslide generation in northwestern Argentina},
  issn      = {1029-7006},
  year      = {2000},
  abstract  = {Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Quantitative analysis of cross recurrence plots were developed to compare the influence of the El Nino/Southern Oscillation (ENSO) on present and past rainfall variations. This analysis has shown the stronger influence of NE trades in the location of landslide deposits in the intra-andean basin and valleys, what caused a higher contrast between summer and winter rainfall and an increasing of precipitation in La Nina years. This is believed to reduce thresholds for landslide generation in the arid to semiarid intra-andean basins and valleys.},
  language  = {en}
}
@article{MarwanTrauthSchwarzetal.1999,
  author    = {Marwan, Norbert and Trauth, Martin H. and Schwarz, Udo and Kurths, J{\"u}rgen and Strecker, Manfred},
  title     = {Climate dynamics of varved pleistocene lake sediments in nw Argentina},
  issn      = {1029-7006},
  year      = {1999},
  language  = {en}
}
@article{MalikBookhagenMarwanetal.2012,
  author    = {Malik, Nishant and Bookhagen, Bodo and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {39},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  number    = {3-4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-011-1156-4},
  pages     = {971 -- 987},
  year      = {2012},
  abstract  = {We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June-September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades.},
  language  = {en}
}
@article{MarwanBellerFelsenbergetal.2012,
  author    = {Marwan, Norbert and Beller, Gise and Felsenberg, Dieter and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {quantifying changes in the spatial structure of trabecular bone},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {22},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127412500277},
  pages     = {12},
  year      = {2012},
  abstract  = {We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.},
  language  = {en}
}
@article{GoswamiMarwanFeulneretal.2013,
  author    = {Goswami, Bedartha and Marwan, Norbert and Feulner, Georg and Kurths, J{\"u}rgen},
  title     = {How do global temperature drivers influence each other?},
  series = {European physical journal special topics},
  volume    = {222},
  journal   = {European physical journal special topics},
  number    = {3-4},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2013-01889-8},
  pages     = {861 -- 873},
  year      = {2013},
  abstract  = {We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.},
  language  = {en}
}
@article{MarwanSchinkelKurths2013,
  author    = {Marwan, Norbert and Schinkel, Stefan and Kurths, J{\"u}rgen},
  title     = {Recurrence plots 25 years later -Gaining confidence in dynamical transitions},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {101},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/101/20007},
  pages     = {6},
  year      = {2013},
  abstract  = {Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.},
  language  = {en}
}
@misc{HempelKoseskaNikoloskietal.2017,
  author    = {Hempel, Sabrina and Koseska, Aneta and Nikoloski, Zoran and Kurths, J{\"u}rgen},
  title     = {Unraveling gene regulatory networks from time-resolved gene expression data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-400924},
  pages     = {26},
  year      = {2017},
  abstract  = {Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.},
  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{MarwanKurths2005,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Line structures in recurrence plots},
  issn      = {0375-9601},
  year      = {2005},
  abstract  = {Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time- transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements. (C) 2005 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{MarwanTrauthVuilleetal.2003,
  author    = {Marwan, Norbert and Trauth, Martin H. and Vuille, Mathias and Kurths, J{\"u}rgen},
  title     = {Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods},
  year      = {2003},
  abstract  = {Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26°S, 66°W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Ni{\~n}o/ Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.},
  language  = {en}
}
@article{MarwanWesselMeyerfeldtetal.2002,
  author    = {Marwan, Norbert and Wessel, Niels and Meyerfeldt, Udo and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Recurrence-plot-based measures of complexity and its application to heart-rate-variability data},
  year      = {2002},
  abstract  = {The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.},
  language  = {en}
}
@article{DongesDonnerTrauthetal.2011,
  author    = {Donges, Jonathan and Donner, Reik Volker and Trauth, Martin H. and Marwan, Norbert and Schellnhuber, Hans Joachim and Kurths, J{\"u}rgen},
  title     = {Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution},
  series = {Proceedings of the National Academy of Sciences of the United States of America},
  volume    = {108},
  journal   = {Proceedings of the National Academy of Sciences of the United States of America},
  number    = {51},
  publisher = {National Acad. of Sciences},
  address   = {Washington},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1117052108},
  pages     = {20422 -- 20427},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@article{DongesZouMarwanetal.2009,
  author    = {Donges, Jonathan and Zou, Yong and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Complex networks in climate dynamics : comparing linear and nonlinear network construction methods},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2009-01098-2},
  year      = {2009},
  abstract  = {Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.},
  language  = {en}
}
@unpublished{EngbertScheffczykKrampeetal.1997,
  author    = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Rosenblum, Mikhael and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Tempo-induced transitions in polyrhythmic hand movements},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14380},
  year      = {1997},
  abstract  = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.},
  language  = {en}
}
@misc{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Generating Surrogates from Recurrences},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56906},
  year      = {2006},
  abstract  = {In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.},
  language  = {en}
}
@article{ScheffczykEngbertKurthsetal.1995,
  author    = {Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold},
  title     = {Nonlinear Phenomena in Polyrhythmic Hand Movements},
  isbn      = {981-02-2689-6},
  year      = {1995},
  abstract  = {In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.},
  language  = {en}
}
@article{EngbertScheffczykKrampeetal.2002,
  author    = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Symbolic dynamics of bimanual production of polyrhythms},
  isbn      = {3-540- 63481-9},
  year      = {2002},
  abstract  = {We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.},
  language  = {en}
}
@article{ScheffczykKrampeEngbertetal.1997,
  author    = {Scheffczyk, Christian and Krampe, Ralf-Thomas and Engbert, Ralf and Rosenblum, Michael and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Tempo-induced transitions in polyrhythmic hand movements},
  year      = {1997},
  abstract  = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.},
  language  = {en}
}
@article{SchiekScheffczykEngbertetal.1997,
  author    = {Schiek, Michael and Scheffczyk, Christian and Engbert, Ralf and Kurths, J{\"u}rgen and Krampe, Ralf-Thomas and Kliegl, Reinhold and Drepper, Friedhelm R.},
  title     = {Symbolic dynamics of physiological synchronisation : examples from bimanual movements and cardiorespiratory interaction},
  year      = {1997},
  abstract  = {Key words: Nonlinear time series analysis, symbolic dynamics, phase transitions, physiological data, biological synchronization, production of polyrhythms, cardiorespiratory interaction, variation of control parameter},
  language  = {en}
}
@article{OrgisBrandSchwarzetal.2009,
  author    = {Orgis, Thomas and Brand, Sascha and Schwarz, Udo and Handorf, D{\"o}rthe and Dethloff, Klaus and Kurths, J{\"u}rgen},
  title     = {Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2009-01105-8},
  year      = {2009},
  abstract  = {A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex.},
  language  = {en}
}