Phase oscillators with sinusoidal coupling interpreted in terms of projective geometry
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 0218-1274Full text not available from this repository.
Official URL: http://dx.doi.org/10.1142/S0218127411029446
Marvel et al.  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.|
|Official Date:||June 2011|
|Page Range:||pp. 1795-1804|
|Access rights to Published version:||Restricted or Subscription Access|
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