Synchronization of Globally Coupled Nonlinear Oscillators

The Rich Behavior of the Kuramoto Model

Bryan Daniels
Spring 2005






Introduction to Synchronization

An example of spontaneous synchronization:
   
picture of metronomes
Synchronization of Metronomes Video (.avi, 3.7 mb)


The phenomenon of synchronization is all around us.  It is found in:

In my research, I looked at self-sustained oscillators.  A self-sustained oscillator:

Self-sustained oscillator
A self-sustained oscillator at three levels of abstraction.  First, the real physical oscillator, in this case a metronome.  Second, the limit cycle in phase space.  Third, we have abstracted away everything about the oscillator except its natural frequency, its phase, and the time derivative of its phase.


With a large group of oscillators, spontaneous synchronization can happen with:



Next Section: The Kuramoto Model