@article{GoldobinPikovskij2006,
  author    = {Goldobin, Denis S. and Pikovskij, Arkadij},
  title     = {Antireliability of noise-driven neurons},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.061906},
  year      = {2006},
  abstract  = {We demonstrate, within the framework of the FitzHugh-Nagumo model, that a firing neuron can respond to a noisy driving in a nonreliable manner: the same Gaussian white noise acting on identical neurons evokes different patterns of spikes. The effect is characterized via calculations of the Lyapunov exponent and the event synchronization correlations. We construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations. Geometrically, the antireliability is described by a random noninvertible one-dimensional map},
  language  = {en}
}
@article{SchwabedalPikovskij2010,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij},
  title     = {Effective phase description of noise-perturbed and noise-induced oscillations},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2010-01271-6},
  year      = {2010},
  abstract  = {An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.},
  language  = {en}
}
@article{SchwabedalPikovskij2010,
  author    = {Schwabedal, Justus T. C. and Pikovskij, Arkadij},
  title     = {Effective phase dynamics of noise-induced oscillations in excitable systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.81.046218},
  year      = {2010},
  abstract  = {We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.},
  language  = {en}
}
@book{FreudeKuznetsovPikovskij2006,
  author    = {Freude, Ulrike and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Strange nonchaotic attractors : dynamics between order and chaos in Quasiperiodically Forced Systems},
  publisher = {World Scientific},
  address   = {Singapore},
  isbn      = {981-256633-3},
  pages     = {350 S.},
  year      = {2006},
  language  = {en}
}