You should use the Logistic Growth With Harvesting Tool in IDE to do this assignment.

For each question, an appropriate graph will help your exposition. You may print this from the computer, or draw carefully by hand what you are seeing on the screen.

1. Set the harvesting rate h to 0.2. What are the equilibrium populations? Which are stable, which unstable? What does this say about the long term implications of this harvesting rate? (Be sure to discuss the outcomes for all possible initial populations.)
2. Set the harvesting rate at 0.4 and answer the same questions.
3. If you have done problems 1 and 2 correctly, you will have quite different outcomes in the two cases. Find the value of h at which the change occurs. You may find this experimentally, but should then prove analytically that the value you have found is correct and explain why. (Note: This is an example of a bifurcation.)