@article{KraemerHellmannAnvarietal.2022,
  author    = {Kr{\"a}mer, Kai Hauke and Hellmann, Frank and Anvari, Mehrnaz and Kurths, J{\"u}rgen and Marwan, Norbert},
  title     = {Spike spectra for recurrences},
  series = {Entropy : an international and interdisciplinary journal of entropy and information studies},
  volume    = {24},
  journal   = {Entropy : an international and interdisciplinary journal of entropy and information studies},
  number    = {11},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {1099-4300},
  doi       = {10.3390/e24111689},
  pages     = {18},
  year      = {2022},
  abstract  = {In recurrence analysis, the tau-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. We introduce a novel method to decompose the tau-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization. We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.},
  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}
}