Phase oscillators with sinusoidal coupling interpreted in terms of projective geometry
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. 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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