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Relaxation Oscillators:

 

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Vibe:Relaxation Oscillators

Perhaps the most important relaxation oscillator is the original van der Pol oscillator. It is implemented here from van Der Pol's 1928 paper (which is recommended reading for anyone who is interested in this topic). Also included is a van der Pol oscillator with forcing.

The Rayleigh oscillator is also important because it responds differently to voltage increases than the van Der Pol oscillator. As voltage incrases, the van Der Pol oscillator increases in frequency whereas the Rayleigh oscillator increases in amplitude. Peter Beek of the Free University of Amsterdam has had some interesting things to say about this. Also, a Ralyeigh oscillator with forcing is included to compare with the forced version of the van Der Pol oscillator.

Two models of the neuron fall into the category of relaxation oscillator. They are very similar, with the primary difference being in how voltage integration is handled. The Fitzhugh-Nagumo Neuron is a two-variable simplification of the Hodgkin-Huxley four-variable equations for the behavior of a neuron.

One might ask, why simplify the Hodgkin-Huxley equations to begin with? The answer lies in the fact that computing differential equations across four variables is extremely time consuming. Also, the authors of these models believe they have captured certain important aspects of neural firing without the need of the extra two variables (Occam's razor).


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Thu Jul 24 09:12:34 EDT 2003