title: Low dimensional behavior of large systems of globally coupled oscillators.
abstract: It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.
authors.affiliation: University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Ott
authors.forename: Thomas M
authors.initials: TM
authors.lastname: Antonsen
mesh_terms: D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback; D053858:Metabolic Networks and Pathways / Q000502:physiology*; D008962:Models, Theoretical; D009415:Nerve Net / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*