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Question (total=10p)
Consider the following difference equation model:
Xt - 2x1_1 + X1-141-1- 5x1-1
(1)
yt = 2y _1 + X1-191-1 - 5y1-1
(2)
1. [2p] Find all its equilibrium points.
2. [2p] Calculate the Jacobian matrix at the equilibrium point (0,0) and at the equilibrium
point where x > 0 and y > 0.
3. [2p] Calculate the eigenvalues of each of the matrices obtained in part 2 of this question.
4. [2p] Based on these results, discuss the stability of the equilibrium point (0,0) and of the
equilibrium point where x > 0 and y > 0.
5. [2p] Develop a continuous-time model analogous to the discrete-time model considered in
this question.
Hints:
. Use the sample meshgrid code below to plot phase space trajectories for the continuous-time system
developed in part 5 of this question and to confirm your findings.
. The phase-space plot of the associated continuous-time system found in part 5 will have the same
equilibrium points and will show similar behaviour at the equilibrium point with x > 0 and y > 0,
but not at (0,0).

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