The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on N-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization. In this paper, the moments systems are introduced for both of the Kuramoto model and its continuous model. It is shown that the moments systems for both systems take the same form. This fact allows one to prove that the order parameter of the N-dimensional Kuramoto model converges to that of the continuous model as N → ∞.
|Number of pages||13|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - May 1 2013|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics