# Kuramoto Model for Phase Locking of Coupled Oscillators

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows the collective synchronization of coupled oscillators according to the Kuramoto model [1], which is a modified version of the Winfree model [2] for the population of biological oscillators.

[more]
Contributed by: Jessica Alfonsi (September 2016)

Padova, Italy

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: weak coupling parameter , incoherent behavior

Snapshot 2: critical coupling parameter , onset of partial synchronization, but incoherent behavior is still present

Snapshot 3: strong coupling parameter , synchronization reached after a short transient, order parameter close to 1

References

[1] Y. Kuramoto, *Chemical Oscillations, Waves and Turbulence*, Berlin: Springer-Verlag, 1984.

[2] A. T. Winfree, *The Geometry of Biological Time*, New York: Springer-Verlag, 1980.

[3] S. H. Strogatz, "From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators," *Physica D: Nonlinear Phenomena*, 143(1–4), 2000 pp. 1–20. doi:10.1016/s0167-2789(00)00094-4.

[4] J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort and R. Spigler, "The Kuramoto Model: A Simple Paradigm for Synchronization Phenomena," *Reviews of Modern Physics*, 77(1), 2005 pp. 137–185. doi:10.1103/RevModPhys.77.137.

## Permanent Citation