Species Competition

Eduardo Sontag's species competition equations using JOde, for classroom use, Rutgers.
Student Assignment:

1. Honor part - no hand-in: Enjoy looking at the initial screen, with direction field and a few trajectories shown. Click at a few random points on the plotting window to see where trajectories go to. (Can you find an initial condition that takes you to the equilibrium in the middle? Pretty hard to do, because it is unstable!)
2. The equations model a "competition" between two species (two species of animals, two types of molecules in a cell, etc.).
   Answer in project to be returned: What two terms in the equations represent this "competition"?
3. Answer in project to be returned: The particular parameters shown correspond to what is called "competitive exclusion".
   Explain why one uses this term. (What happens to 'x' and 'y' in steady state?)
4. "Clear all" and un-select "slopes" so that the screen looks clean.
5. Set now m=1;n=1;a=2;h=1;b=2;k=1 and click "submit all".
   Now click at about 10 random places in the screen, and see what the trajectories look like.
6. Print (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. (If you have difficulties printing, you can always try a "print screen"; most computers allow you to do that.)
7. Explain why we call this situation "coexistence".
8. Now clear and set m=1;n=1;a=1;h=2;b=1;k=0.5, submit all.
   Now click at about 10 random places in the screen, and see what the trajectories look like.
   Answer: what happens now?
   Print.
9. Find parameters so that all solutions have the property that y always wins. Now click at about 10 random places in the screen, and see what the trajectories look like.
   Print.