@article{SchwabedalPikovskij2013,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij},
  title     = {Phase description of stochastic oscillations},
  series = {Physical review letters},
  volume    = {110},
  journal   = {Physical review letters},
  number    = {20},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.110.204102},
  pages     = {5},
  year      = {2013},
  abstract  = {We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The approach allows us to obtain a global phase variable of noisy oscillations, even in the cases where the phase is ill defined in the deterministic limit. A simple numerical method for finding the isophases is illustrated for noise-induced switching between two coexisting limit cycles, and for noise-induced oscillation in an excitable system. We also discuss how to determine isophases of observed irregular oscillations, providing a basis for a refined phase description in data analysis.},
  language  = {en}
}