Chaos and Images (Page 6)

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The following two movies demonstrate the emergence of coherence in the Kuramoto system. In the Kuramoto system, a large number of phase oscillators are globally coupled to each other through a meanfield variable. The system is initialized in a incoherent state and the parameters are chosen so that the system will tend to the coherent state after a transient.
A Ring of Phase Oscillators

by Stepan Kruglikov - animated (avi)

Top: Phase Oscillators initially distributed uniformly around the circle cluster into a single group
Bottom: The situation as seen through the Kuramoto order parameter (phasor average of the oscillators)

Phase Oscillators as Colored Dots

by Paul So - animated (avi)

The phase value of the an oscillator in [0,2p] is mapped to a particular color in the spectrum. Clusters of coherence forms when the coupling strength is above a certain threshold and the size of the cluster grows with the strength of coupling. With the coupling chosen not too far above the critical value in this simulation, one can see that the really fast and slow blinkers do not synchronize.

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