@article{GoldobinPikovskij2005,
  author    = {Goldobin, Denis S. and Pikovskij, Arkadij},
  title     = {Synchronization and desynchronization of self-sustained oscillators by common noise},
  year      = {2005},
  abstract  = {We consider the effect of external noise on the dynamics of limit cycle oscillators. The Lyapunov exponent becomes negative under influence of small white noise, what means synchronization of two or more identical systems subject to common noise. We analytically study the effect of small nonidentities in the oscillators and in the noise, and derive statistical characteristics of deviations from the perfect synchrony. Large white noise can lead to desynchronization of oscillators, provided they are nonisochronous. This is demonstrated for the Van der Pol-Duffing system},
  language  = {en}
}
@article{GoldobinPikovskij2005,
  author    = {Goldobin, Denis S. and Pikovskij, Arkadij},
  title     = {Synchronization of self-sustained oscillators by common white noise},
  year      = {2005},
  abstract  = {We study the stability of self-sustained oscillations under the influence of external noise. For small-noise amplitude a phase approximation for the Langevin dynamics is valid. A stationary distribution of the phase is used for an analytic calculation of the maximal Lyapunov exponent. We demonstrate that for small noise the exponent is negative, which corresponds to synchronization of oscillators. (c) 2004 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{RosenauPikovskij2005,
  author    = {Rosenau, Philip and Pikovskij, Arkadij},
  title     = {Phase compactons in chains of dispersively coupled oscillators},
  issn      = {0031-9007},
  year      = {2005},
  abstract  = {We study the phase dynamics of a chain of autonomous oscillators with a dispersive coupling. In the quasicontinuum limit the basic discrete model reduces to a Korteveg-de Vries-like equation, but with a nonlinear dispersion. The system supports compactons: solitary waves with a compact support and kovatons which are compact formations of glued together kink-antikink pairs that may assume an arbitrary width. These robust objects seem to collide elastically and, together with wave trains, are the building blocks of the dynamics for typical initial conditions. Numerical studies of the complex Ginzburg-Landau and Van der Pol lattices show that the presence of a nondispersive coupling does not affect kovatons, but causes a damping and deceleration or growth and acceleration of compactons},
  language  = {en}
}
@article{ZillmerPikovskij2005,
  author    = {Zillmer, R{\"u}diger and Pikovskij, Arkadij},
  title     = {Continuous approach for the random-field Ising chain},
  year      = {2005},
  abstract  = {We study the random-field Ising chain in the limit of strong exchange coupling. In order to calculate the free energy we apply a continuous Langevin-type approach. This continuous model can be solved exactly, whereupon we are able to locate the crossover between an exponential and a power-law decay of the free energy with increasing coupling strength. In terms of magnetization, this crossover restricts the validity of the linear scaling. The known analytical results for the free energy are recovered in the corresponding limits. The outcomes of numerical computations for the free energy are presented, which confirm the results of the continuous approach. We also discuss the validity of the replica method which we then utilize to investigate the sample-to-sample fluctuations of the finite size free energy},
  language  = {en}
}