@article{KliemSchwarzKurthsetal.1998,
  author    = {Kliem, Bernhard and Schwarz, Udo and Kurths, J{\"u}rgen and Dennis, Brian and Schwartz, Richard and Aschwanden, Markus J.},
  title     = {Wavelet analysis of solar flare hard X-ray},
  issn      = {0004-637x},
  year      = {1998},
  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{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{AnishchenkoNikolaevKurths2006,
  author    = {Anishchenko, Vadim S. and Nikolaev, S and Kurths, J{\"u}rgen},
  title     = {Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.056202},
  year      = {2006},
  abstract  = {We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place},
  language  = {en}
}