Stewart, Ian, 1945-. (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. ISSN 0218-1274

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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
Date:	June 2011
Volume:	Vol.21
Number:	No.6
Page Range:	pp. 1795-1804
Identification Number:	10.1142/S0218127411029446
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/38465

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