@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{MontbrioKurthsBlasius2004,
  author    = {Montbrio, Ernest and Kurths, J{\"u}rgen and Blasius, Bernd},
  title     = {Synchronization of two interacting populations of oscillators},
  year      = {2004},
  abstract  = {We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.},
  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}
}
@article{VossTimmerKurths2004,
  author    = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen},
  title     = {Modeling and identification of nonlinear systems},
  issn      = {0218-1274},
  year      = {2004},
  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{BeimGrabenSaddyKurths2004,
  author    = {Beim Graben, Peter and Saddy, Douglas and Kurths, J{\"u}rgen},
  title     = {Untitled},
  year      = {2004},
  language  = {de}
}
@article{LindTitzKuhlbrodtetal.2004,
  author    = {Lind, P. G. and Titz, Sven Holger and Kuhlbrodt, Till and Corte-Real, J. A. M. and Kurths, J{\"u}rgen and Gallas, J. A. C. and Feudel, Ulla},
  title     = {Coupled bistable maps : a tool to study convection parameterization in ocean models},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells. For large diffusion our model exhibits a phase transition from convective patterns to a homogeneous state over the entire lattice. In hysteresis experiments we find staircase behavior depending on stability thresholds of local convection patterns. This nonphysical behavior is suspected to induce spurious abrupt changes in the spreading of convection in ocean models. The final steady state of convective cells depends not only on the magnitude of the advective velocity but also on its direction, implying a possible bias in the development of convective patterns. Such bias points to the need for an appropriate choice of grid geometry in ocean modeling},
  language  = {en}
}
@article{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {Testing for phase synchronization},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series},
  language  = {en}
}
@article{GamezZhouTimmermannetal.2004,
  author    = {Gamez, A. J. and Zhou, Changsong and Timmermann, A. and Kurths, J{\"u}rgen},
  title     = {Nonlinear dimensionality reduction in climate data},
  issn      = {1023-5809},
  year      = {2004},
  abstract  = {Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Nino-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO},
  language  = {en}
}
@article{BoveBoccalettiBragardetal.2004,
  author    = {Bove, I. and Boccaletti, Stefano and Bragard, Jean and Kurths, J{\"u}rgen and Mancini, H.},
  title     = {Frequency entrainment of nonautonomous chaotic oscillators},
  year      = {2004},
  abstract  = {We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty},
  language  = {en}
}