@article{KuptsovKuznetsovPikovskij2013,
  author    = {Kuptsov, Pavel V. and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Hyperbolic chaos at blinking coupling of noisy oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {87},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.87.032912},
  pages     = {7},
  year      = {2013},
  abstract  = {We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where onecluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations. DOI: 10.1103/PhysRevE.87.032912},
  language  = {en}
}
@article{IsaevaKuznetsovKuznetsov2013,
  author    = {Isaeva, Olga B. and Kuznetsov, Alexey S. and Kuznetsov, Sergey P.},
  title     = {Hyperbolic chaos of standing wave patterns generated parametrically by a modulated pump source},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {87},
  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.87.040901},
  pages     = {4},
  year      = {2013},
  abstract  = {We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales 1 : 3. DOI: 10.1103/PhysRevE.87.040901},
  language  = {en}
}