@article{KralemannPikovskijRosenblum2011,
  author    = {Kralemann, Bj{\"o}rn and Pikovskij, Arkadij and Rosenblum, Michael},
  title     = {Reconstructing phase dynamics of oscillator networks},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {21},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.3597647},
  pages     = {10},
  year      = {2011},
  abstract  = {We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.},
  language  = {en}
}
@article{SchwabedalPikovskijKralemannetal.2012,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij and Kralemann, Bj{\"o}rn and Rosenblum, Michael},
  title     = {Optimal phase description of chaotic oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {85},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.85.026216},
  pages     = {9},
  year      = {2012},
  abstract  = {We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincare surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rossler and Lorenz systems.},
  language  = {en}
}
@article{KralemannPikovskijRosenblum2013,
  author    = {Kralemann, Bj{\"o}rn and Pikovskij, Arkadij and Rosenblum, Michael},
  title     = {Detecting triplet locking by triplet synchronization indices},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {87},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.87.052904},
  pages     = {6},
  year      = {2013},
  abstract  = {We discuss the effect of triplet synchrony in oscillatory networks. In this state the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. We suggest an easy to compute measure, a triplet synchronization index, which can be used to detect such states from experimental data.},
  language  = {en}
}