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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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