@article{BraunPikovskijMatiasetal.2012,
  author    = {Braun, W. and Pikovskij, Arkadij and Matias, M. A. and Colet, P.},
  title     = {Global dynamics of oscillator populations under common noise},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {99},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/99/20006},
  pages     = {6},
  year      = {2012},
  abstract  = {Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that at the initial stage, the order parameter grows linearly in time, while at the later stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles with the Lorentzian distribution of natural frequencies and determine the stationary values of the order parameter in dependence on driving noise and mismatch.},
  language  = {en}
}
@article{KuptsovKuznetsovPikovskij2012,
  author    = {Kuptsov, Pavel V. and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Hyperbolic chaos of turing patterns},
  series = {Physical review letters},
  volume    = {108},
  journal   = {Physical review letters},
  number    = {19},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.108.194101},
  pages     = {4},
  year      = {2012},
  abstract  = {We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation longwave and shortwave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.},
  language  = {en}
}
@article{MulanskyPikovskij2012,
  author    = {Mulansky, Mario and Pikovskij, Arkadij},
  title     = {Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {86},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.86.056214},
  pages     = {7},
  year      = {2012},
  abstract  = {In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find a nice agreement of the scaling predicted from the NDE with the spreading results from extensive numerical studies. Moreover, we show that the scaling works also for regular lattices with strongly nonlinear coupling, for which the scaling exponent is estimated analytically. This shows that the process of chaotic diffusion in such lattices does not require disorder.},
  language  = {en}
}
@article{RoyPikovskij2012,
  author    = {Roy, S. and Pikovskij, Arkadij},
  title     = {Spreading of energy in the Ding-Dong model},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {22},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.3695369},
  pages     = {7},
  year      = {2012},
  abstract  = {We study the properties of energy spreading in a lattice of elastically colliding harmonic oscillators (Ding-Dong model). We demonstrate that in the regular lattice the spreading from a localized initial state is mediated by compactons and chaotic breathers. In a disordered lattice, the compactons do not exist, and the spreading eventually stops, resulting in a finite configuration with a few chaotic spots.},
  language  = {en}
}
@article{SchwabedalPikovskijKralemannetal.2012,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij and Kralemann, Bj{\"o}rn and Rosenblum, Michael},
  title     = {Optimal phase description of chaotic oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {85},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.85.026216},
  pages     = {9},
  year      = {2012},
  abstract  = {We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincare surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rossler and Lorenz systems.},
  language  = {en}
}