# one dimensional noisy ODE as a first passage problem
f(x)=x^2+I
wiener w
trial'=0
x'=f(x)+sig*w
global 0 t {x=xreset}
par xreset=-10,sig=.2,I=0
@ total=1000,meth=euler,bound=10000
done
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1. Run this program
2. Numerics Poincare Section X, 10 , stop-on-section=y
3. Escape to main menu
4. Initconds Range Trial, 2000 steps, 0 to 2000, Go
5. You will now have the times that x spiked - plot T vs Trial to
see them all
6. Stochastics Stat variable:t will give mean and std dev
mean=18.13, std dev=11.2, CV = sd/mean = .6
7. Stochastic Histogram - 100 bins min:0 max:100 variable:t
(ignore condition). Escape to main menu
8.Click Xi vs t and choose TRIAL to plot. You will get a histogram
9. Graphics Freeze Freeze - fill in as you want - this keeps the
curve
change parameters, eg, I or noise and repeat this, or keep parameters the
same to see if the sme form appears. For example, show that doubling the
noise makes the ISI shorter and the histogram narrower! Change the
noise to 0.2 and I=-.1. You may want to make the histogram have more bins
and a larger maximum value (400 eg)
what does the CV do as I changes from say -0.2 to 0.2