This post is motivated by the Joy Of X and a video lecture given by Professor Strogatz in which he introduces the Kuramoto model for synchronization of random harmonic oscillators. This continues a theme of contemplations or pointing to resources such as the wonderful story on a Mobius strip.

I made the following animated gif hastily in Mathematica and, perhaps, if time permits I will contemplate a better CDF (including rotating frame to better illustrate the frequency locking as well as the “rogue” oscillators”). Ten harmonic oscillators with frequencies derived from a normal distribution (1,1)[ scale/units not represented in gif). Varying coupling strength is illustrated.

There a number of poor aspects to the animation. Unfortunately, to make the file size smaller I compromise the number of cycles rather than image size. Consequently, the jerky effect (given the frequency locking develops rather than a constant angular frequency). This lack of cycles prevents appreciation of the development of frequency locking within a given coupling strength.

Oh well, a public trial and error iteration…

Categories: Mathematica, Mathematics
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