@article{KomarovPikovskij2013,
  author    = {Komarov, Maxim and Pikovskij, Arkadij},
  title     = {Multiplicity of singular synchronous States in the kuramoto model of coupled oscillators},
  series = {Physical review letters},
  volume    = {111},
  journal   = {Physical review letters},
  number    = {20},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.111.204101},
  pages     = {5},
  year      = {2013},
  abstract  = {We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.},
  language  = {en}
}
@article{KomarovPikovskij2013,
  author    = {Komarov, Maxim and Pikovskij, Arkadij},
  title     = {Dynamics of multifrequency oscillator communities},
  series = {Physical review letters},
  volume    = {110},
  journal   = {Physical review letters},
  number    = {13},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.110.134101},
  pages     = {5},
  year      = {2013},
  abstract  = {We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The simplest situation of three resonantly interacting groups is analyzed in detail. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations and present examples where the interaction between communities leads to their synchrony or to a partially asynchronous state or to a chaotic dynamics of order parameters. DOI: 10.1103/PhysRevLett.110.134101},
  language  = {en}
}