Skip to main content

Stochastic synchronization

  • Synchronization And Stochastic Resonance
  • Conference paper
  • First Online:
Stochastic Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 484))

Abstract

The fundamental phenomenon of synchronization occurs in non-linear self-sustained oscillators subjected to a periodic force or coupled with each other. This phenomenon manifests itself in locking or suppressing of the natural frequency of the oscillator by periodic force. In this paper we discuss surprising synchronization-like phenomena in stochastic bistable systems which have no natural frequency at all. Stochastic bistable system possesses a noise-controlled mean switching frequency between metastable states being an analogy of natural frequency. The stochastic synchronization reveals locking of the mean switching frequency by external periodic force. The same phenomenon can be observed in coupled stochastic bistable systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Andronov A.A., Vitt A.A., and Khaikin S.E. (1966): Theory of Oscillators, Pergamon, Oxford

    MATH  Google Scholar 

  • Andronov A.A., Leontovich E.A., Gordon I.I., and Maier A.G. (1973): Qualitative Theory of Second-Order Dynamic Systems, Wiley, New York

    MATH  Google Scholar 

  • Afraimovich V.S., Verichev N.N., and Rabinovich M.I. (1986): Stochastically synchronized oscillations in dissipative systems, Izvestija Vuzov, Radiofizika, 29, 1050–1060

    ADS  MathSciNet  Google Scholar 

  • Anishchenko V.S., Vadivasova T.E., Postnov D.E., and Safonova M.A. (1992): Synchronization of chaos, Int.Journal of Bifurcation and Chaos, 2N3, 633–644

    Article  MathSciNet  Google Scholar 

  • Arnold V.I. (1979): Loss of stability of oscillations near the resonances. In: Nonlinear Waves. A.V. Gaponov-Grechov ed., 116–130, Nauka Publisher, Moscow

    Google Scholar 

  • Berge P., Pomeau Y., and Vidal (1988): Ch., L'ordre Dans le Chaos. Versune Approache Deterministe de la Turbulence, Hermann ed.

    Google Scholar 

  • Benzi R., Sutera S., and Vulpiani A. (1981): The mechanism of stochastic resonance, J.Phys. A14, L454–L457

    MathSciNet  Google Scholar 

  • Bulsara A., Chillemi S., Kiss L., McClintock P.V.E., Mannella R., Marchesoni F., Nikolis K., and Wiesenfeld K., editors (1995): Proc. of the International Workshop on fluctuations in physics and biology: Stochastic resonance, signal Processing and related phenomena, Nuovo Cimento D17

    Google Scholar 

  • Bulsara A., and Gammaitoni L. (1996): Tuning in to noise, Physics Today, March, 39–44

    Google Scholar 

  • Dykman M.I., McClintock P.V.E., Mannella R., and Stocks N.G. (1990): Stochastic resonance in the linear and nonlinear responses of a bistable system to a periodic field, Soviet Phys JETP Lett. 52, 141–143

    ADS  Google Scholar 

  • Fauve S., and Heslot F. (1983): Stochastic resonance in a bistable system, Phys.Lett. A97, 5–7

    ADS  Google Scholar 

  • Gammaitoni L., Marchesoni F., and Santucci S. (1995): Stochastic resonance as a bona fide resonance, Phys.Rev.Lett. 74, 1052–1055

    Article  ADS  Google Scholar 

  • Haken H. (1983): Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices, Springer, Berlin

    MATH  Google Scholar 

  • Hänggi P., Talkner P., and Borkovec M. (1990): Reaction-rate theory: Fifty years after Kramers, Rev.Mod.Phys. 62, 251–341

    Article  ADS  Google Scholar 

  • Hayashi Ch. (1964): Nonlinear Oscillation in physical systems, McCraw-hill book company

    Google Scholar 

  • Jung P., Periodically driven stochastic systems, Phys.Rep. 234, 175–295

    Google Scholar 

  • Jung P., and Hänggi P. (1991): Amplification of small signals via stochastic resonance, Phys.Rev. A44, 8032–8042

    ADS  Google Scholar 

  • Malchow H., and Schimansky-Geier L. (1984): Noise and Diffusion in Bistable Nonequilibrium Systems, Teubner-Texte, Leipzig

    Google Scholar 

  • McNamara B., and Wiesenfeld K. (1989): Theory of stochastic resonance, Phys.Rev. A39, 4854

    ADS  Google Scholar 

  • Moss F., Bulsara A., and Shlesinger M.F., editors (1993): Proc. NATO ARW on stochastic resonance in physics and biology, J.Stat.Phys. 70, 1–512

    Google Scholar 

  • Moss F., Pierson D., and O'Gorman D. (1994): Stochastic resonance: tutorial and update, Int. Journal of Bifurcation and Chaos 4, 1383–1397

    Article  MATH  MathSciNet  Google Scholar 

  • Neiman A. (1994): Synchronizationlike phenomena in coupled stochastic bistable systems, Phys.Rev. E49, 3485–3488

    ADS  Google Scholar 

  • Neiman A., Shulgin B., Anishchenko V., Ebeling W., Schimansky-Geier L., and Freund J. (1996): Dynamical entropies applied to stochastic resonance, Phys.Rev.Lett. 76, 4299–4301

    Article  ADS  Google Scholar 

  • Pecora L.M., and Carroll T.J. (1990): Synchronization in chaotic systems, Phys.Lett. A64, 821–824

    Article  MathSciNet  Google Scholar 

  • Rosenblum M.G., Pikovsky A.S., and Kurths J. (1996): Phase synchronization of chaotic oscillators, Phys.Rev.Lett. 76 1804–1807

    Article  ADS  Google Scholar 

  • Shulgin B., Neiman A., and Anishchenko V. (1995): Mean switching frequency locking in stochastic bistable systems driven by a periodic force, Phys.Rev.Lett. 75, 4157–4160

    Article  ADS  Google Scholar 

  • Stocks N.G. (1995): A theoretical study of the non-linear response of a periodically driven bistable system, Nuovo Cimento D17 925–940

    Article  ADS  Google Scholar 

  • Wiesenfeld K., and Moss F. (1995): Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs, Nature 373, 33–36

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Lutz Schimansky-Geier Thorsten Pöschel

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag

About this paper

Cite this paper

Anishchenko, V.S., Neiman, A.B. (1997). Stochastic synchronization. In: Schimansky-Geier, L., Pöschel, T. (eds) Stochastic Dynamics. Lecture Notes in Physics, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105607

Download citation

  • DOI: https://doi.org/10.1007/BFb0105607

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62893-4

  • Online ISBN: 978-3-540-69040-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics