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Phase synchronization of chaotic rotators.

Grigory V Osipov1, Arkady S Pikovsky, Jürgen Kurths

  • 1Institute of Physics, University Potsdam, 10, Am Neuen Palais, D-14415 Potsdam, Germany.

Physical Review Letters
|February 28, 2002
PubMed
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We show phase synchronization in chaotic rotators, where Lyapunov exponents stay positive. This frequency-locked dynamics transition occurs through a crisis leading to a band-structured attractor.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Statistical Mechanics

Background:

  • Phase synchronization is a key phenomenon in coupled chaotic systems.
  • Previous studies on chaotic oscillators showed Lyapunov exponents becoming non-positive upon synchronization.
  • Understanding synchronization in rotators is crucial for various physical systems.

Purpose of the Study:

  • To demonstrate phase synchronization in two coupled chaotic rotators.
  • To investigate the behavior of Lyapunov exponents in this synchronous regime.
  • To characterize the transition mechanism to phase synchronization.

Main Methods:

  • Analysis of driven continuous-time rotators.
  • Study of discrete circle maps.
  • Examination of Lyapunov exponents and attractor structures.

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Main Results:

  • Phase synchronization was demonstrated in two chaotic rotators.
  • Lyapunov exponents for both phases remained positive even during synchronization.
  • The transition to phase synchronization was observed to occur via a crisis leading to a band-structured attractor.

Conclusions:

  • Chaotic rotators exhibit a unique form of phase synchronization.
  • The positive Lyapunov exponents indicate a complex, non-trivial synchronous state.
  • The crisis-induced transition to a band-structured attractor provides insight into synchronization dynamics.