- 2 Set A 1 So The System Becomes Q Du 02 0 U 8 Du Dt By U Dt A Find All The Critical Points And Investi 1 (9.78 KiB) Viewed 23 times
(a) Find all the critical points, and investigate their (linear) stability, as the param- eters 8 and 8 are varied. [3 marks] (b) For this part, set B = 0. Show that the v axis is invariant. Find the phase flow on this invariant axis. [1 marks] (c) For this part, set B = 2. Note that if d = 0, the origin is a critical point, and find its linear stability. Investigate the bifurcation as 8 crosses the value 0 (Note that the system is not in normal form). [2 marks] (d) For this part, set B = 2. Use the (Dulac) function g(u, v) = 42(v-u) to show that the system has no periodic orbits for some values of 8. [1 mark]