@article{KrishnanBazhenovPikovskij2013,
  author    = {Krishnan, Giri Panamoottil and Bazhenov, Maxim and Pikovskij, Arkadij},
  title     = {Multipulse phase resetting curves},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {88},
  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.88.042902},
  pages     = {9},
  year      = {2013},
  abstract  = {In this paper, we introduce and study systematically, in terms of phase response curves, the effect of dual-pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from linear summation of phase advances resulting from two small perturbations. We analytically derive a correction term, which generally appears for oscillators whose intrinsic dimensionality is >1. The nonlinear correction term is found to be proportional to the square of the perturbation. We demonstrate this effect in the Stuart-Landau model and in various higher dimensional neuronal models. This deviation from the superposition principle needs to be taken into account in studies of networks of pulse-coupled oscillators. Further, this deviation could be used in the verification of oscillator models via a dual-pulse excitation.},
  language  = {en}
}