For the system
x = x + y + 1
y = 2x - y + 5
(i) Find the fixed point.
(ii) Transform the system into deviations from the fixed point. What are the characteristic roots of this transformed system?
(iii) Derive the equations for the stable and unstable arms.
(iv) Set the model up on a spreadsheet and plot, on the same graph, the following trajectories:
(a) The trajectory from initial point (- 2,4).
(b) The unstable arm passing through the point at which x =2.