Consider the logistic differential equation (Section 5.1, Exercise 27) with harvesting proportional to population size, or db/dt = b(1 - b - h) where h represents the fraction harvested. Graph the equilibria as functions of h for values of h between 0 and 2, using a solid line when an equilibrium is stable and a dashed line when an equilibrium is unstable. Even though they do not make biological sense, include negative values of the equilibria on your graph. You should find a transcritical bifurcation (Exercise 17) at h = 1.
Exercises 17-20 show how the number and stability of equilibria can change when a parameter changes. Often, bifurcations have important biological applications, and bifurcation diagrams help in explaining how the dynamics of a system can suddenly change when a parameter changes only slightly. In each case, graph the equilibria against the parameter value, using a solid line when an equilibrium is stable and a dashed line when an equilibrium is unstable to draw the bifurcation diagram.