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Frequency spirals.

Bertrand Ottino-Löffler1, Steven H Strogatz1

  • 1Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

Localized spatiotemporal patterns called "frequency spirals" were discovered in coupled phase oscillators. These novel patterns exhibit librating motion, unlike stationary or rotating spirals seen in other systems.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Coupled phase oscillators are fundamental to understanding synchronization phenomena.
  • The Kuramoto model describes synchronization in networks of interacting oscillators.
  • Spatiotemporal patterns in oscillator networks are crucial for diverse applications.

Purpose of the Study:

  • To investigate novel localized spatiotemporal patterns in a 2D Kuramoto lattice.
  • To characterize the unique dynamics of these patterns, termed 'frequency spirals'.
  • To analyze the behavior of frequency spirals near the phase-locking transition.

Main Methods:

  • Simulations on a two-dimensional Kuramoto lattice with periodic boundary conditions.
  • Analysis of instantaneous frequencies and phase representations of oscillators.
  • Analytical and numerical methods to construct and characterize frequency spirals.

Main Results:

  • Discovery of localized spatiotemporal patterns named 'frequency spirals' below the global phase-locking transition.
  • Frequency spirals manifest as two-armed rotating structures in the instantaneous frequency domain.
  • These patterns exhibit librating motion around a phase vortex, distinct from stationary or rotating spirals.
  • A simple prototype frequency spiral was constructed and its properties characterized.

Conclusions:

  • Frequency spirals represent a new class of collective behavior in coupled oscillator systems.
  • Their unique librating dynamics offer insights into complex pattern formation.
  • Simulations confirm that large lattices exhibit behavior consistent with the prototype frequency spiral.