Here is an XPP file for computing
first passage times for a simple scalar neuron model. The figure
shows some histograms for (red I=0,sigma=0.2;green I=0,sigma=0.4; white
I=-.1,sigma=.2)
Here is an XPP file for computing
the FI curve for a simple scalar neuron model. The plot shows
the FI curve as sigma goes from 0 to 0.5.
Here is a very complex XPP file to solve
the first passage BVP using AUTO. The plot shows the results of this
for sigma=1 and 0.1 Note AUTO has a bit of a problem when I is negative and
large.
The FI curve with noise can be approximated by the following
function. Let F(I) be the deterministic curve and define
L(x,b) =x/(1-exp(-b*x))
As b gets large, L(x,b) approaches the curve max(x,0). So, 1/b is like
the amount of noise and FI(I) = F(L(I,b)) is a decent fit. We will
use something like this later when we create firing rate models.
Noise related homework: page 153: 1,2 (computer exercise);4,6,8
Neural oscillators
Start reading the chapter on oscillators
HOMEWORK: oscillator chapter: 7,23,26,27. I'd assign many more, but
you wouldnt do 'em anyway.