@article{ToenjesPikovsky2020,
  author    = {T{\"o}njes, Ralf and Pikovsky, Arkady},
  title     = {Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.052315},
  pages     = {5},
  year      = {2020},
  abstract  = {We study ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.},
  language  = {en}
}
@article{GongToenjesPikovsky2020,
  author    = {Gong, Chen Chris and T{\"o}njes, Ralf and Pikovsky, Arkady},
  title     = {Coupled M{\"o}bius maps as a tool to model Kuramoto phase synchronization},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.022206},
  pages     = {12},
  year      = {2020},
  abstract  = {We propose Mobius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.},
  language  = {en}
}