This question considers the famous Lotka-Volterra model of competition between two species, hereafter imagined to be humans and aliens. Suppose that both species are competing for the same food supply and the amount available is limited. The two main effects we will consider are: 1. Each species would grow to its carrying capacity in the absence of the other. This can remodeled by assuming logistic growth for each species. Aliens have a legendary ability to reproduce, so perhaps we should assign them a higher intrinsic growth rate. 2. When aliens and humans encounter each other, trouble starts. Sometimes the alien gets to eat, but more usually the human nudges the alien aside and start nibbling (on the food, that is). We'll assume that these conflicts occur at a rate proportional to the size of each population. (If there were twice as many humans, the odds of an alien encountering a human would be twice as great.) Furthermore, we assume that the conflicts reduce the growth rate for each species, but the effect is more severe for the aliens. A specific model that incorporates these assumptions is x = x(3 − x - y), y = y(2 - x - y), where x is the population of aliens and y is the population of humans. Sketch the phase portrait by completing the following steps. Assume x ≥ 0 and y ≥ 0.
1. Find and classify the fixed points.
2. Draw the nullclines
3. Fill in representative trajectories using the classification of the fixed points.

4. Check your work using the pplane applet.