Frequency spirals
Abstract
We study the dynamics of coupled phase oscillators on a twodimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phaselocking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as twoarmed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reactiondiffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.
 Authors:
 Center for Applied Mathematics, Cornell University, Ithaca, New York 14853 (United States)
 Publication Date:
 OSTI Identifier:
 22596658
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 9; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY CONDITIONS; OSCILLATORS; PERIODICITY; SIMULATION; TWODIMENSIONAL CALCULATIONS
Citation Formats
OttinoLöffler, Bertrand, and Strogatz, Steven H., Email: strogatz@cornell.edu. Frequency spirals. United States: N. p., 2016.
Web. doi:10.1063/1.4954038.
OttinoLöffler, Bertrand, & Strogatz, Steven H., Email: strogatz@cornell.edu. Frequency spirals. United States. doi:10.1063/1.4954038.
OttinoLöffler, Bertrand, and Strogatz, Steven H., Email: strogatz@cornell.edu. 2016.
"Frequency spirals". United States.
doi:10.1063/1.4954038.
@article{osti_22596658,
title = {Frequency spirals},
author = {OttinoLöffler, Bertrand and Strogatz, Steven H., Email: strogatz@cornell.edu},
abstractNote = {We study the dynamics of coupled phase oscillators on a twodimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phaselocking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as twoarmed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reactiondiffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.},
doi = {10.1063/1.4954038},
journal = {Chaos (Woodbury, N. Y.)},
number = 9,
volume = 26,
place = {United States},
year = 2016,
month = 9
}

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