@article{Pikovskij2021,
  author    = {Pikovskij, Arkadij},
  title     = {Transition to synchrony in chiral active particles},
  series = {Journal of physics. Complexity},
  volume    = {2},
  journal   = {Journal of physics. Complexity},
  number    = {2},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {2632-072X},
  doi       = {10.1088/2632-072X/abdadb},
  pages     = {8},
  year      = {2021},
  abstract  = {I study deterministic dynamics of chiral active particles in two dimensions. Particles are considered as discs interacting with elastic repulsive forces. An ensemble of particles, started from random initial conditions, demonstrates chaotic collisions resulting in their normal diffusion. This chaos is transient, as rather abruptly a synchronous collisionless state establishes. The life time of chaos grows exponentially with the number of particles. External forcing (periodic or chaotic) is shown to facilitate the synchronization transition.},
  language  = {en}
}
@article{Pikovskij2021,
  author    = {Pikovskij, Arkadij},
  title     = {Synchronization of oscillators with hyperbolic chaotic phases},
  series = {Izvestija vysšich učebnych zavedenij : naučno-techničeskij žurnal = Izvestiya VUZ. Prikladnaja nelinejnaja dinamika = Applied nonlinear dynamics},
  volume    = {29},
  journal   = {Izvestija vysšich učebnych zavedenij : naučno-techničeskij žurnal = Izvestiya VUZ. Prikladnaja nelinejnaja dinamika = Applied nonlinear dynamics},
  number    = {1},
  publisher = {Saratov State University},
  address   = {Saratov},
  issn      = {0869-6632},
  doi       = {10.18500/0869-6632-2021-29-1-78-87},
  pages     = {78 -- 87},
  year      = {2021},
  abstract  = {Topic and aim. Synchronization in populations of coupled oscillators can be characterized with order parameters that describe collective order in ensembles. A dependence of the order parameter on the coupling constants is well-known for coupled periodic oscillators. The goal of the study is to extend this analysis to ensembles of oscillators with chaotic phases, moreover with phases possessing hyperbolic chaos. Models and methods. Two models are studied in the paper. One is an abstract discrete-time map, composed with a hyperbolic Bernoulli transformation and with Kuramoto dynamics. Another model is a system of coupled continuous-time chaotic oscillators, where each individual oscillator has a hyperbolic attractor of Smale-Williams type. Results. The discrete-time model is studied with the Ott-Antonsen ansatz, which is shown to be invariant under the application of the Bernoulli map. The analysis of the resulting map for the order parameter shows, that the asynchronouis state is always stable, but the synchronous one becomes stable above a certain coupling strength. Numerical analysis of the continuous-time model reveals a complex sequence of transitions from an asynchronous state to a completely synchronous hyperbolic chaos, with intermediate stages that include regimes with periodic in time mean field, as well as with weakly and strongly irregular mean field variations. Discussion. Results demonstrate that synchronization of systems with hyperbolic chaos of phases is possible, although a rather strong coupling is required. The approach can be applied to other systems of interacting units with hyperbolic chaotic dynamics.},
  language  = {en}
}