Tuesday, December 23, 2008

Diffusively coupled oscillators

Having previously seen the effects that oscillators near 180 degree phase-boundaries run faster, I conducted the experiment of isolating two oscillators and varying the diffusive constant between them (thanks John). This first graph shows the time trace of the two diffusively-coupled oscillators started 180 degrees out of phase. Note how both amplitude and wavelength are different early-on compared to later when the two have synchronized. The next graph shows the peak frequency of the first phase (before phase lock) as a function of diffusion.

I know this is a well-known phenomena and is the basis of reaction diffusion systems so I started hunting for references. First google hit was: PRL 96 054101 - Daido and Nakanishi - Diffusion Induced Inhomogeneity in Globally Coupled Oscillators. They show various facets of a similar system without regard to spatial dynamics (like this experiment). They refernce Erik's father's (A T Winfree) book The Geometry of Biological Time which looks like a must read. They also reference an interesting sounding book: Synchronization - A Universal Concept in Nonlinear Sciences which looks like another must read and the UT library has an online copy!

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