2009/02/28 by Edward Ott, Thomas M. Antonsen · 19 citations
Computer Science · Physics and Astronomy · #Attractor #Center manifold #Chaos control and synchronization #Dynamical systems theory #Invariant manifold #Manifold (fluid mechanics) #Nonlinear Dynamics and Pattern Formation #Oscillation (cell signaling) #Phase (matter) #Slow manifold #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.3136851
Improved discussion of Eqs. (28)- (30) Corrected typos. Made notation consistent
arxiv created 2009/04/16 · openalex publication_date 2009/05/19 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.