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Related Experiment Videos

Phase synchronization in the forced Lorenz system.

E H Park1, M A Zaks, J Kurths

  • 1Institute of Physics, Potsdam University, Postfach 601553, D-14415 Potsdam, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Phase synchronization in chaotic systems with periodic forcing hinges on intrinsic timescales. Perfect synchronization is unattainable for the Lorenz attractor, leading to "imperfect phase synchronization" with alternating frequency lockings.

Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Statistical physics

Background:

  • Phase synchronization is a key phenomenon in chaotic systems.
  • Periodic forcing can influence synchronization dynamics.
  • The Lorenz attractor exhibits complex dynamics with unbounded return times.

Purpose of the Study:

  • To investigate the influence of intrinsic characteristic times on phase synchronization in chaotic systems under weak periodic forcing.
  • To analyze the conditions for perfect and imperfect phase synchronization.
  • To examine the behavior of the Lorenz attractor under periodic forcing.

Main Methods:

  • Analysis of unstable periodic orbits.
  • Characterization of frequency locking ratios.
  • Examination of phase dynamics under periodic forcing.

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Main Results:

  • Phase synchronization dynamics critically depend on the distribution of intrinsic characteristic times.
  • For systems with nearly isochronous chaotic rotations, all periodic orbits exhibit the same locking ratio.
  • The Lorenz attractor displays "imperfect phase synchronization" characterized by alternating temporal segments with different rational frequency lockings.

Conclusions:

  • The distribution of intrinsic timescales dictates phase synchronization in forced chaotic systems.
  • Perfect phase synchronization is not achievable for systems like the Lorenz attractor.
  • Imperfect phase synchronization emerges as a distinct state in such systems, featuring intermittent rational frequency lockings.