Year: 2009
Type: article
Abstract: It is shown, under weak conditions, that the dynamical evolution of large systems of globally coupled phase oscillators with Lorentzian distributed oscillation frequencies is, in an appropriate physical sense, time-asymptotically attracted toward a reduced manifold of the system states. This manifold was previously known and used to facilitate the discovery of attractors and bifurcations of such systems. The result of this paper establishes that attractors for the order parameter dynamics obtained by restriction to this reduced manifold are, in fact, the only such attractors of the full system. Thus all long time dynamical behaviors of the order parameters of these systems can be obtained by restriction to the reduced manifold.
DOI: 10.1063/1.3136851
Authors: Edward Ott, Thomas M. Antonsen
Institution: University of Maryland, College Park
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1996106850