Answer: 17 through 19 deal with competitive systems much like those in Examples 1 and 2

Chapter 9, Problem 17

(choose chapter or problem)

17 through 19 deal with competitive systems much like those in Examples 1 and 2, except that some coefficients depend on a parameter . In each of these problems assume that x, y, and are always nonnegative. In each of 17 through 19: (a) Sketch the nullclines in the first quadrant, as in Figure 9.4.5. For different ranges of your sketch may resemble different parts of Figure 9.4.5. (b) Find the critical points. (c) Determine the bifurcation points. (d) Find the Jacobian matrix J and evaluate it for each of the critical points. (e) Determine the type and stability property of each critical point. Pay particular attention to what happens as passes through a bifurcation point (f) Draw phase portraits for the system for selected values of to confirm your conclusions.