Given the nonlinear system P˙ = rP − R(h)

h˙ = g(P) − (d + n)h

(i) Derive the linear approximation about (P∗, h∗).

(ii) Assume R

(h∗) = −0.5 r = 0.05 n = 0.01 g

(P∗) = 1 d = 0.02 and that the system is initially in equilibrium at P∗ = 1 and h∗ = 1.

Show that the two isoclines through this equilibrium are P˙ = 0 implying P = 11 − 10h h˙ = 0 implying P = 0.97 + 0.03h

(iii) Show that the characteristic values of the system are r = 0.7182 and s = −0.6982 and hence verify that (P∗, h∗) = (1, 1) is a saddle path equilibrium.