(a) Sketch a phase portrait for the system

˙ x = x(4 − y − x), ˙ y = y(3x − 1 − y), x ≥ 0, y≥ 0, given that the critical points occur at O = (0, 0), A = (4, 0), and B = (5/4, 11/4).

(b) Sketch a phase portrait for the system

˙ x = x(2 − y − x), ˙ y = y(3 − 2x − y), x ≥ 0, y≥ 0, given that the critical points occur at O = (0, 0), C = (0, 3), D =

(2, 0), and E = (1, 1).

82 3. Interacting Species One of the systems can be used to model predator–prey interactions and the other competing species. Describe which system applies to which model and interpret the results in terms of species behavior.