Synchronization of Coupled Phase Oscillators

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

In 1665, Huygens discovered that two pendula suspended side-by-side eventually synchronize. Today it is known that synchronization is a common feature of interacting oscillatory systems. This Demonstration visualizes the synchronization of coupled phase oscillators. The plot shows the time variation of the oscillator frequencies. When the coupling constant is 0, there is no interaction between the oscillators, so each oscillator has a different frequency. As the coupling constant increases, you can observe synchronization. It turns out that the synchronization frequency is the average of the initial frequencies.

Contributed by: Baris Altunkaynak (March 2011)
Open content licensed under CC BY-NC-SA



The equations of motion are given by the coupled differential equations:


where is the number of oscillators, is the coupling constant, and is the phase of the oscillator.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.