Phase synchronization of chaotic oscillators by external driving

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Abstract

We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed. and the phase dynamics of a single self-sustanined chaotic oscillator subjected to external force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the external force. This effect is demonstrated for periodic and noisy driving. This phase synchronization is characterized via direct calculation of the phase, as well as by implicit indications, such as the resonant growth of the discrete component in the power spectrum and the appearance of a macroscopic average field in an ensemble of driven oscillators. The Rössler and the Lorenz systems are shown to provide examples of different phase coherence properties, with different response to the external force. A relation between the phase synchronization and the properties of the Lyapunov spectrum is discussed.

References (44)

  • E.F. Stone

    Phys. Lett. A

    (1992)
  • L. Brunnet et al.

    Physica D

    (1994)
  • O.E. Rössler

    Phys. Lett. A

    (1976)
  • C. Hugenii

    Horoloqium Oscilatorium

    (1673)
  • A. Andronov et al.

    Theory of Oscillations

    (1966)
  • C. Hayashi

    Nonlinear Oscillations in Physical Systems

    (1964)
  • I. Blekhman

    Synchronization of Dynamical Systems

    (1981)
  • I. Blekhman

    Synchronization in Science and Technology

    (1981)
  • H. Fujisaka et al.

    Progr. Theoret. Phys.

    (1983)
  • A.S. Pikovsky

    Z. Physik B

    (1984)
  • L.M. Pecora et al.

    Phys. Rev. Lett.

    (1990)
  • P.S. Landa et al.

    Sov. Phys. Dokl.

    (1992)
  • P.S. Landa et al.

    Appl. Mech. Rev.

    (1993)
  • Y. Kuznetsov et al.

    Sov. Phys. Dokl.

    (1985)
  • L. Kocarev et al.

    Int. J. Bifurc. and Chaos

    (1993)
  • L. Bezaeva et al.

    Zhurnal Tekhnicheskoi Fiziki

    (1987)
  • G. Dykman et al.

    Chaos, Solitons and Fractals

    (1992)
  • P. Landa et al.

    Electronics

    (1985)
  • V. Anischenko et al.

    Int. J. Bifurc. and Chaos

    (1992)
  • M. Rosenblum et al.

    Phys. Rev. Lett.

    (1996)
  • A.S. Pikovsky

    Soviet J. Comm. Tech. Electronics

    (1985)
  • A. Pikovsky et al.

    Europhys. Lett.

    (1996)
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    1

    Alexander von Humboldt Fellow on leave from Mechanical Engineering Research Institut, Russian Acad. Sci., Moscow, Russian Federation.

    2

    Permanent address: Radiophysical Department, Nizhni Novgorod University, Nizhni Novgorod, Russian Federation.

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