ODE Hodgkin-Huxley JOde Example
Eduardo Sontag's Hodgin-Huxley equations using JOde, for classroom use.
I is the applied current (for a more interesting problem, make it a function!)
Am, etc are the alphas; Bm, etc the betas
gm, etc are the conductances
Em, etc the reversal potentials
u is the voltage
C (capacitance) has been set to one
- Try various integer values for the applied current, I = 1, 2, 3, ... so
that you find the largest value I for which only one voltage spike is produced
(don't forget to "Submit All" each time that you change the current, so the
program runs again!).
Print two pictures: one of the plot with this "I" that you found, and one of the plot with "I+1".
As the current is set respectively to the values 10, 20, 30, 40, 50, 60,
the amplitude of the spikes remains roughly constant, but the number of
spikes changes ("frequency modulation"); report how many spikes you see for
each of these 6 values (in the window from t=0 to t=100).
Bring the value of "I" again to the original 15.1
Now display only "n" and "h" (click on them and un-select "u"). Observe that
n(t)+h(t) add up to a
constant; report what is the value (approximately) of that constant.
Explain how this relates to something discussed in the notes (someone observed
something that allows a nice reduction to a 2D system... who was that?)
Important: to see the scales of n and h (not u), you need to change the "u" to
"m" or "h" in the upper right button.)
Now display also "m", besides n and h. Note that "m" changes a bit faster
than n and h, at least during some intervals.
(To see the color of "m" as black, you may change the "u" to "m" in the upper
Provide printouts for all of the above.
(If you have problems printing, see
If all fails, do a "print screen"; most computers allow you to do that.)
Instructions on using the JOde Applet
JOde was written by Marek Rychlik (firstname.lastname@example.org)
Author's Home Page: http://alamos.math.arizona.edu