In this problem we apply a constant-yield model of harvesting to the situation in

Chapter 9, Problem 16

(choose chapter or problem)

In this problem we apply a constant-yield model of harvesting to the situation in Example 1. Consider the system x_ = x(1 0.5y) H1, y_ = y(0.75 + 0.25x) H2, where H1 and H2 are nonnegative constants. Recall that if H1 = H2 = 0, then (3, 2) is an equilibrium solution for this system. a. Before doing any mathematical analysis, think about the situation intuitively. How do you think the populations will change if the prey alone is harvested? if the predator alone is harvested? if both are harvested? b. How does the equilibrium solution change if the prey is harvested ( H1 > 0), but not the predator ( H2 = 0)? c. How does the equilibrium solution change if the predator is harvested ( H2 > 0), but not the prey ( H1 = 0)? d. How does the equilibrium solution change if both predator and prey are harvested ( H1 > 0, H2 > 0)?