The Ramsey model can be reduced to a pair of simultaneous differential equations. In general, systems of simultaneous differential equations can have a variety of stability properties. Below are two abstract examples of pairs of simultaneous differential equations. For each one, draw the phase diagram and comment on the systems stability properties as revealed by the diagram. (Note that both examples have a steady state at x = 0, y = 0. Negative, as well as positive, values of x and y should be considered.)

(a) x' = y - x y' = x - 2y

(b) x' = x - y y' = x + y