Chemostat

Eduardo Sontag's chemostat equations using JOde, for classroom use.
Student Assignment:

1. Enjoy looking at the initial screen, with direction field and a few trajectories shown.
2. "Clear all" and un-select "slopes" so that the screen looks clean.
3. Now click at a about 10 random places in the screen, and see what the trajectories look like.
4. (A) Print and submit the printout, labeled "A" (note: the program gives you the option to print to file and save for later printing or emailing). Use the Print button in the applet, NOT the one for the browser.
5. Clear all.
6. Plot the solution with N(0)=2 and C(0)=3.5 (you may use the "additional initial condition" and click "submit" next to it, or just click in the appropriate place on the screen).
7. (B) Print and submit the printout, labeled "B".
8. (C) Plot both C(t) and N(t) against t, and print (you can obtain this plot by using the button right under the plot window and selecting "t" as the x-axis, and also clicking on "N" in the y-axis so that the plot for N displays at the same time as the one for C).
9. (D) Explain in words what the model predicts. (A couple of English sentences like" bacteria increase while nutrient increases, until so and so happens..")
10. Clear all. Go back to the phase plane (C in vertical, N in horizontal).
11. Now set a2=0.5 and click "submit all".
12. Plot the solution with N(0)=2 and C(0)=3.5 (you may use the "additional initial condition" or just click in an appropriate place on the screen).
13. (E) Print.
14. What happened to the positive steady state? Explain using theory!
15. (F) Plot C(t) and N(t) against t and print (you can obtain this plot by using the button right under the plot window and selecting "t" as the x-axis).
16. (G) Explain in words what the model predicts. Will bacterial population decrease from time t=0? Will there be some time interval when it increases? What happens to the nutrient concentration? Does it always decrease? If not, how can you explain what you see?
    (Use two paragraphs in grammatical English. If your handwriting is poor, please type.)