@article{SchwabedalPikovskij2010,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij},
  title     = {Effective phase description of noise-perturbed and noise-induced oscillations},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2010-01271-6},
  year      = {2010},
  abstract  = {An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.},
  language  = {en}
}
@article{SchwabedalPikovskij2010,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij},
  title     = {Effective phase dynamics of noise-induced oscillations in excitable systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.81.046218},
  year      = {2010},
  abstract  = {We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.},
  language  = {en}
}