@article{VasconcelosLopesVianaetal.2006,
  author    = {Vasconcelos, D. B. and Lopes, S. R. and Viana, R. L. and Kurths, J{\"u}rgen},
  title     = {Spatial recurrence plots},
  doi       = {10.1103/Physreve.73.056207},
  year      = {2006},
  abstract  = {We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes},
  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{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{AbelAhnertKurthsetal.2005,
  author    = {Abel, Markus and Ahnert, Karsten and Kurths, R. and Mandelj, S.},
  title     = {Additive nonparametric reconstruction of dynamical systems from time series},
  issn      = {1063-651X},
  year      = {2005},
  abstract  = {We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential},
  language  = {en}
}
@article{WesselKonvickaWeidermannetal.2004,
  author    = {Wessel, Niels and Konvicka, Jan and Weidermann, Frank and Nestmann, S. and Neugebauer, R. and Schwarz, U. and Wessel, A. and Kurths, J{\"u}rgen},
  title     = {Predicting thermal displacements in modular tool systems},
  issn      = {1054-1500},
  year      = {2004},
  abstract  = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally inducedaccuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems. errors can be estimated with 1-2 micrometer},
  language  = {en}
}
@article{WesselAssmusWeidermannetal.2004,
  author    = {Wessel, Niels and Aßmus, Joerg and Weidermann, Frank and Konvicka, Jan and Nestmann, S. and Neugebauer, R. and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {Modeling thermal displacements in modular tool systems},
  year      = {2004},
  abstract  = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally induced errors can be estimated with 1-2\${mu m}\$ accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.},
  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{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{SureshSenthilkumarLakshmananetal.2010,
  author    = {Suresh, R. and Senthilkumar, Dharmapuri Vijayan and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen},
  title     = {Global phase synchronization in an array of time-delay systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.82.016215},
  year      = {2010},
  abstract  = {We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.},
  language  = {en}
}
@article{WesselKleinerVossetal.1997,
  author    = {Wessel, Niels and Kleiner, H. J. and Voss, Andreas and Kurths, J{\"u}rgen and Dietz, R.},
  title     = {Nonlinear dynamics in cardiovasscular diseases},
  year      = {1997},
  language  = {en}
}
@article{AgarwalMaheswaranKurthsetal.2016,
  author    = {Agarwal, Ankit and Maheswaran, Rathinasamy and Kurths, J{\"u}rgen and Khosa, R.},
  title     = {Wavelet Spectrum and Self-Organizing Maps-Based Approach for Hydrologic Regionalization -a Case Study in the Western United States},
  series = {Water Resources Management},
  volume    = {30},
  journal   = {Water Resources Management},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0920-4741},
  doi       = {10.1007/s11269-016-1428-1},
  pages     = {4399 -- 4413},
  year      = {2016},
  abstract  = {Hydrologic regionalization deals with the investigation of homogeneity in watersheds and provides a classification of watersheds for regional analysis. The classification thus obtained can be used as a basis for mapping data from gauged to ungauged sites and can improve extreme event prediction. This paper proposes a wavelet power spectrum (WPS) coupled with the self-organizing map method for clustering hydrologic catchments. The application of this technique is implemented for gauged catchments. As a test case study, monthly streamflow records observed at 117 selected catchments throughout the western United States from 1951 through 2002. Further, based on WPS of each station, catchments are classified into homogeneous clusters, which provides a representative WPS pattern for the streamflow stations in each cluster.},
  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{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}
}