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Phase oscillators with sinusoidal coupling interpreted in terms of projective geometry
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Stewart, Ian (2011) Phase oscillators with sinusoidal coupling interpreted in terms of projective geometry. International Journal of Bifurcation and Chaos, Vol.21 (No.6). pp. 1795-1804. doi:10.1142/S0218127411029446 ISSN 0218-1274.
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Official URL: http://dx.doi.org/10.1142/S0218127411029446
Abstract
Marvel et al. [2009] studied sinusoidally coupled phase oscillators, generalizing coupled Josephson junctions. They obtained an explicit reduction of the dynamics to a parametrised family of ODEs on the three-dimensional Mobius group. This differs from the usual reduction on to the orbit space of a symmetry group. We apply the viewpoint of complex projective geometry to obtain an alternative proof that trajectories lie on orbits of the Mobius group, and derive a different explicit form for the reduced ODE. The main innovation is the use of homogeneous coordinates, which linearize the action of the Mobius group and lead to a simple coordinate system in which to write the reduced ODE. We also discuss a Lie-theoretic interpretation.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Möbius transformations, Coordinates, Differential equations, Geometry, Projective | ||||
Journal or Publication Title: | International Journal of Bifurcation and Chaos | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-1274 | ||||
Official Date: | June 2011 | ||||
Dates: |
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Volume: | Vol.21 | ||||
Number: | No.6 | ||||
Page Range: | pp. 1795-1804 | ||||
DOI: | 10.1142/S0218127411029446 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Data sourced from Thomson Reuters' Web of Knowledge
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