@article{BlahaPikovskijRosenblumetal.2011,
  author    = {Blaha, Karen A. and Pikovskij, Arkadij and Rosenblum, Michael and Clark, Matthew T. and Rusin, Craig G. and Hudson, John L.},
  title     = {Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {84},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.84.046201},
  pages     = {7},
  year      = {2011},
  abstract  = {Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.},
  language  = {en}
}