Problem 1:
a.  From the class website, go to John Polking's dfield website and download the appropriate versions of pplane5.m and ppn5out.m.  pplane5 is a Matlab program which is a great help in visualizing and analyzing two-dimensional systems of ODEs.  It can find steady states, evaluate their stability, draw nullclines and plot trajectories.

b.  Try your hand at pplane5 by using it to examine the Chemostat equations (Edelstein-Keshet p.193, eqs. 18a,b), choosing parameters for which there is a stable steady state.  Draw nullclines, identify steady states and sketch sample trajectories.   Please include a printout of your results.

c.  Now do Edelstein-Keshet p.203, #13.
 

Problem 2:
a. Edelstein-Keshet p.158, #27.

b. For further analysis, do Edelstein-Keshet p.206, #18 (you may employ pplane5 to check your analysis).
 

Problem 3:
a. Edelstein-Keshet p.303, #17.

b. Use pplane5 to verify your analysis in part a.