• Using the ordered set model of partial orders (each partial order can be view as a set of ordered pairs), explore the proof of Axion 1.3 using Venn diagrams.
• Read O, p. 40-46
• Do problems 12,13,14,16,17 on p. 48 of O.
• Read O, p. 100, p. 105-113.
• Do problems 9,12,13,18,19,23 on p. 113 of O
• Read Ch. 3 of K&S, do #8

Quiz 4, due Wednesday Feb. 6th

1. Do problems 13 and 14 on p. 48 of O
2. Suppose that we make one of the equations in the competitive hunters model a logistic growth model (ie, one of the hunters has a natural limitation to its population size). So the equations are the following :
   dx/dt = a(M-x)-bxy and dy/dt = py-cxy
   Find the equilibrium points and stability lines (or curves). Explore the direction of trajectories around the equilibium points (you do not need to use Taylor Series, just see what you can determine with signs of the derivatives). Will the system be stable? Does it depend on starting levels of population? Interpret your results as best you can. (Note that there are at least two alternatives depending on whether M>p/c or not. Look at these two cases).