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The European Physical Journal Special Topics

, Volume 222, Issue 10, pp 2481–2495 | Cite as

Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation

  • Anna ZakharovaEmail author
  • Alexey Feoktistov
  • Tatyana Vadivasova
  • Eckehard Schöll
Regular Article Nonlinear Dynamics of Stochastic Systems

Abstract

We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system.

Keywords

Hopf Bifurcation European Physical Journal Special Topic Noise Intensity Deterministic System Unstable Limit Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • Anna Zakharova
    • 1
    Email author
  • Alexey Feoktistov
    • 2
  • Tatyana Vadivasova
    • 2
  • Eckehard Schöll
    • 1
  1. 1.Institut für Theoretische Physik, Technische Universität BerlinBerlinGermany
  2. 2.Saratov State UniversitySaratovRussia

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