UCCS Department of Mathematics
Graduate Student Presentation
SPRING 2008

Jeff Marsh

Title:

The Kuramoto Model

Abstract:

The Kuramoto Model describes the behavior of a large population of
weakly-coupled, nearly identical oscillators. It has been used to explain the
self-synchronization of heart pacemaker cells, the metaboloic cycles
of yeast cells, and the flashing of fireflies.

 \frac{\partial \theta_i}{\partial t} = \omega_i + \frac{K}{N} \sum_{j=1}^{N} \sin(\theta_j - \theta_i), \qquad i = 1 \ldots N