Format

Send to

Choose Destination
Chaos. 2008 Sep;18(3):037113. doi: 10.1063/1.2930766.

Low dimensional behavior of large systems of globally coupled oscillators.

Author information

1
University of Maryland, College Park, Maryland 20742, USA.

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.

PMID:
19045487
DOI:
10.1063/1.2930766
[Indexed for MEDLINE]

Supplemental Content

Full text links

Icon for American Institute of Physics
Loading ...
Support Center