@article{PereiraBaptistaReyesetal.2009,
  author    = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo B. and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen},
  title     = {A scenario for torus T-2 destruction via a global bifurcation},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2007.06.115},
  year      = {2009},
  abstract  = {We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T-2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type- if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.},
  language  = {en}
}
@article{ZaikinKurths2000,
  author    = {Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Additive noise and noise-induced nonequilibrium phase transitions},
  isbn      = {1-563-96826-6},
  year      = {2000},
  language  = {en}
}
@article{ZaikinKurths2001,
  author    = {Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Additive noise in noise-induced nonequilibrium transitions},
  issn      = {1054-1500},
  year      = {2001},
  language  = {en}
}
@article{ParkRosenblumKurthsetal.1999,
  author    = {Park, Eun Hyoung and Rosenblum, Michael and Kurths, J{\"u}rgen and Zaks, Michael A.},
  title     = {Alternating locking ratios in imperfect phase synchronization},
  year      = {1999},
  language  = {en}
}
@article{KolodnerAbelKurthsetal.1999,
  author    = {Kolodner, P. and Abel, Markus and Kurths, J{\"u}rgen and Voss, Henning U.},
  title     = {Amplitude equations from spatiotemporal binary-fluid convection data},
  year      = {1999},
  language  = {en}
}
@article{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {An approach to multivariate phase synchronization analysis and its application to event-related potentials},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields},
  language  = {en}
}
@misc{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {An approach to multivariate phase synchronization analysis and its application to event-related potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20106},
  year      = {2004},
  abstract  = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.},
  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}
}
@article{ZakharovaKurthsVadivasovaetal.2011,
  author    = {Zakharova, Anna and Kurths, J{\"u}rgen and Vadivasova, Tatyana and Koseska, Aneta},
  title     = {Analysing dynamical behavior of cellular networks via stochastic bifurcations},
  series = {PLoS one},
  volume    = {6},
  journal   = {PLoS one},
  number    = {5},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0019696},
  pages     = {12},
  year      = {2011},
  abstract  = {The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.},
  language  = {en}
}
@article{KomalapriyaRomanoBlascoThieletal.2009,
  author    = {Komalapriya, Chandrasekaran and Romano Blasco, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Simonotto, Jennifer and Furman, Michael and Ditto, William L. and Carney, Paul R.},
  title     = {Analysis of high-resulution microelectrode EEG recordings in an animal model of spontaneous limbic seizures},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127409023226},
  year      = {2009},
  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{ZhouKurthsHu2001,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen and Hu, B.},
  title     = {Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise},
  year      = {2001},
  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{AnishchenkoVadivasovaKurthsetal.2004,
  author    = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kurths, J{\"u}rgen and Okrokvertskhov, G. A. and Strelkova, G. I.},
  title     = {Autocorrelation function and spectral linewidth of spiral chaos in a physical experiment},
  issn      = {1063-651X},
  year      = {2004},
  abstract  = {We present results of physical experiments where we measure the autocorrelation function (ACF) and the spectral linewidth of the basic frequency of a spiral chaotic attractor in a generator with inertial nonlinearity both without and in the presence of external noise. It is shown that the ACF of spiral attractors decays according to an exponential law with a decrement which is defined by the phase diffusion coefficient. It is also established that the evolution of the instantaneous phase can be approximated by a Wiener random process},
  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{FrascaBergnerKurthsetal.2012,
  author    = {Frasca, Mattia and Bergner, Andre and Kurths, J{\"u}rgen and Fortuna, Luigi},
  title     = {Bifurcations in a star-like network of Stuart-Landau oscillators},
  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    = {7},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127412501738},
  pages     = {13},
  year      = {2012},
  abstract  = {In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results.},
  language  = {en}
}
@article{GowinSaparinKurthsetal.2001,
  author    = {Gowin, W. and Saparin, Peter and Kurths, J{\"u}rgen and Felsenberg, D.},
  title     = {Bone Architecture assessment with Measures of Complexity},
  year      = {2001},
  language  = {en}
}
@article{GowinSaparinKurths2001,
  author    = {Gowin, W. and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {Bone architecture quantification: Measures of complexity compared to failure lead results},
  year      = {2001},
  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}
}