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Phase synchronization in noisy and chaotic oscillators

  • Synchronization And Stochastic Resonance
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Stochastic Dynamics

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

Abstract

In this contribution we discuss properties of phase synchronization in noisy and chaotic oscillations. Classical results for the synchronization of periodic self-sustained oscillations subject to a noisy driving are reviewed and compared with recently found phase synchronization effects in chaotic oscillators. Different approaches to the phase definition in chaotic systems, as well as the phase dynamics, are duscussed. Effects of synchronization by external force and mutual synchronization are illustrated with the Rössler and Lorenz systems.

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References

  • Andronov A., Vitt A., Khaykin S. (1966): Theory of Oscillations (Pergamon Press, Oxford)

    Google Scholar 

  • Bezaeva L., Kaptsov L., Landa P. (1986): Synchronization Threshold as the Criterium of Stochasticity in the Generator with Inertial Nonlinearity. Sov.Phys.-Tech.Phys 31, 1105–1107

    Google Scholar 

  • Blekhman I. (1971): Synchronization of Dynamical Systems (Nauka, Moscow), (in Russian).

    Google Scholar 

  • Blekhman I. (1981): Synchronization in Science and Technology (Nauka, Moscow), (in Russian); English translation: (1988), (ASME Press, NY).

    Google Scholar 

  • Blekhman I., Landa P., Rosenblum M. (1995): Synchronization and Chaotization in Interacting Dynamical Systems. Appl. Mech. Rev. 48, 733–752

    Article  Google Scholar 

  • Brunnet L., Chaté H., Manneville P. (1994): Long-Range Order with Local Chaos in Lattices of Diffusively Coupled ODEs. Physica D 78, 141–154

    Article  MATH  ADS  Google Scholar 

  • Dykman G., Landa P., Neymark Yu. (1992): Synchronizing the Chaotic Oscillations by External Force. Chaos, Solitons & Fractals 1, 339–353

    Article  ADS  Google Scholar 

  • Ebeling W., Feistel R. (1982): Physik der Selbstorganisation und Evolution (Akademie Verlag, Berlin)

    Google Scholar 

  • Ebeling W., Engel H., Herzel H. (1990): Selbstorganisation in der Zeit (Akademie Verlag, Berlin)

    Google Scholar 

  • Farmer J., Crutchfield J., Froehling H., Packard N., Shaw R (1980): Power Spectra and Mixing Properties of Strange Attractors. Ann. N. Y. Acad. Sci. 357, 453

    Article  ADS  Google Scholar 

  • Farmer J. (1981): Spectral Broadening of Period-Doubling Bifurcation Sequences. Phys.Rev.Lett 47, 179–182

    Article  ADS  Google Scholar 

  • Freeman W. (1992): Tutorial on Neurobiology: From Single Neurons to Brain Chaos. Int. J. of Bifurcation and Chaos 2, 451–482

    Article  MATH  Google Scholar 

  • Fujisaka H., Yamada T. (1983): Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. Prog.Theor.Phys. 69, 32–47

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Gabor D. (1946): Theory of Communication. J. IEE London 93, 429–457

    Google Scholar 

  • Goryachev A., Kapral R. (1996): Sprial Waves in Chaotic Systems. Phys. Rev. Lett. 76, 1619–1622

    Article  ADS  Google Scholar 

  • Hayashi C (1964): Nonlinear oscillations in physical systems (McGraw-Hill, NY)

    MATH  Google Scholar 

  • Hugenii (Huygens) C. (1673): Horoloqium Oscilatorium (Parisiis, France)

    Google Scholar 

  • Kuznetsov Yu., Landa P., Ol'khovoi A., Perminov S. (1985): Relationship Between the Amplitude Threshold of Synchronization and the Entropy in Stochastic Self-Excited Systems. Sov. Phys. Dokl. 30, 221–222

    ADS  Google Scholar 

  • Landa P., Permonov S. (1985): Interaction of Periodic and Stochastic Self-Oscillations. Electronics 28, 285–287

    Google Scholar 

  • Landa P., Rosenblum M. (1992): Synchronization of Chaotic Self-Oscillatory Systems. Sov. Phys. Dokl. 37, 237–239

    MathSciNet  Google Scholar 

  • Landa P., Rosenblum M. (1993): Synchronization and Chaotization of Oscillations in Coupled Self-Oscillating Systems. Appl. Mech. Rev. 46, 414–426

    Article  Google Scholar 

  • Lorenz E. (1963): Deterministic Nonperiodic Flow. J.Atmos.Sci. 20, 130–141

    Article  ADS  Google Scholar 

  • Osipov G., Pikovsky A., Rosenblum M., Kurths J. (1997): Phase Synchronization Effects in a Lattice of Nonindentical Rössler Oscillators. Phys. Rev. E (in press)

    Google Scholar 

  • Ott E. (1992): Chaos in Dynamical Systems (Cambridge Univ. Press, Cambridge)

    Google Scholar 

  • Panter P. (1965): Modulation, Noise, and Spectral Analysis (McGraw-Hill, NY)

    Google Scholar 

  • Parlitz U., Junge L., Lauterborn W., Kocarev L. (1996): Experimental Observation of Phase Synchronization. Phys. Rev. E. 54, 2115–2118

    Article  ADS  Google Scholar 

  • Pecora L., Carroll T. (1990): Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 821–824

    Article  ADS  MathSciNet  Google Scholar 

  • Pikovsky A. (1984): On the Interaction of Strange Attractors. Z.Physik B 55, 149–154

    Article  MathSciNet  ADS  Google Scholar 

  • Pikovsky A. (1985): Phase Synchronization of Chaotic Oscillations by a Periodic External Field. Sov. J. Commun. Technol. Electron. 30, 85

    Google Scholar 

  • Pikovsky A., Rosenblum M., Kurths J. (1996): Synchronization in a Population of Globally Coupled Chaotic Oscillators. Europhys. Lett. 34, 165–170

    Article  ADS  Google Scholar 

  • Risken H. (1989): The Fokker-Planck Equation (Springer, Berlin)

    MATH  Google Scholar 

  • Rosenblum M.G., Pikovsky A.S., Kurths J. (1996): Phase Synchronization of Chaotic Oscillators. Phys. Rev. Lett. 76, 1804–1807

    Article  ADS  Google Scholar 

  • Rössler O. (1976): An Equation for Continuous Chaos. Phys.Lett.A 57, 397

    Article  ADS  Google Scholar 

  • Shalfeev V. (1982): Use of Cumulant Method in the Investigation of PLL. (in: Shakhgildyan V., Belyustina L. (eds.) Phase Synchronization Systems (Radio i Svjaz, Moscow), pp.95–104, (in Russian))

    Google Scholar 

  • Winful H., Rahman L. (1990): Synchronized Chaos and Spatiotemporal Chaos in Arrays of Coupled Lasers. Phys. Rev. Lett. 65 1575–1578

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Arbeitsgruppe “Nichtlineare Dynamik”, Potsdam University, Am Neuen Palais 10, 14415, Potsdam, Germany

    Michael Rosenblum, Arkady Pikovsky & Jürgen Kurths

Authors
  1. Michael Rosenblum
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  2. Arkady Pikovsky
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  3. Jürgen Kurths
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Editor information

Lutz Schimansky-Geier Thorsten Pöschel

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© 1997 Springer-Verlag

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Rosenblum, M., Pikovsky, A., Kurths, J. (1997). Phase synchronization in noisy and chaotic oscillators. In: Schimansky-Geier, L., Pöschel, T. (eds) Stochastic Dynamics. Lecture Notes in Physics, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105613

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  • DOI: https://doi.org/10.1007/BFb0105613

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62893-4

  • Online ISBN: 978-3-540-69040-5

  • eBook Packages: Springer Book Archive

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