@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{KruglovKuznetsovPikovskij2014,
  author    = {Kruglov, Vyacheslav P. and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Attractor of Smale - Williams type in an autonomous distributed system},
  series = {Regular and chaotic dynamics : international scientific journal},
  volume    = {19},
  journal   = {Regular and chaotic dynamics : international scientific journal},
  number    = {4},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {1560-3547},
  doi       = {10.1134/S1560354714040042},
  pages     = {483 -- 494},
  year      = {2014},
  abstract  = {We consider an autonomous system of partial differential equations for a one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases transformed from one stage of activity to another by the doubly expanding circle map. So, the attractor in the Poincar, section is uniformly hyperbolic, a kind of Smale - Williams solenoid. Finite-dimensional models are derived as ordinary differential equations for amplitudes of spatial Fourier modes (the 5D and 7D models). Correspondence of the reduced models to the original system is demonstrated numerically. Computational verification of the hyperbolicity criterion is performed for the reduced models: the distribution of angles of intersection for stable and unstable manifolds on the attractor is separated from zero, i.e., the touches are excluded. The example considered gives a partial justification for the old hopes that the chaotic behavior of autonomous distributed systems may be associated with uniformly hyperbolic attractors.},
  language  = {en}
}