instructions: Solve each of these problems. Your solution should be complete and written out in complete sentences. Where graphs are needed, you may include a print-out of output from Matlab (or another program, if you prefer). You are encouraged to work with other students, but please note that all work that you submit must be your own. 1. In lab 3 we consider the nonlinear system N = (A N(1 P)), P = P(N 1). In the prelab, you found that the linearized system around the critical point (1, A1) is u = Auv, v = (A 1)u.

(a) Show that the system can be rewritten as the second order ODE y Ay (A 1)y = 0. (Rewrite the system to show that u and v satisfy this ODE).

(b) Let A = 2. Determine the type and stability of the phase portrait for this ODE.

(c) Sketch a phase portrait of each case 0 < < 1 and > 1.