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Synchronization of periodic self-oscillations by common noise

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Abstract

We consider the effect of external noise on the stability properties of self-oscillations. A stochastic equation for the phase is derived at the limit of weak noise (in the appropriate sense). The stationary probability-density distribution is used for an analytic calculation of the Lyapunov exponent. We show that the exponent is always negative for the small noise level, which corresponds to synchronization of self-oscillations.

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Authors and Affiliations

  1. Perm State University, Perm, Rusia

    D. S. Goldobin

  2. University of Potsdam, Potsdam, Germany

    D. S. Goldobin & A. S. Pikovsky

Authors
  1. D. S. Goldobin
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  2. A. S. Pikovsky
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, Nos. 10–11, pp. 1013–1019, October–November, 2004.

D. S. Goldobin acknowledges the support by the Germany-France-Russia Trilateral Project, the “Dynasty” Foundation, and the International Center for Fundamental Physics in Moscow.

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Goldobin, D.S., Pikovsky, A.S. Synchronization of periodic self-oscillations by common noise. Radiophys Quantum Electron 47, 910–915 (2004). https://doi.org/10.1007/s11141-005-0031-8

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  • DOI: https://doi.org/10.1007/s11141-005-0031-8

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