Consider the following two-dimensional difference equations model:
Xt = xt-1 + 2xt-1(1 – xt-1 ) – xt-1 yt-1
Yt = yt-1 + 2yt-1(1 – yt-1 ) – xt-1 yt-1 1.
1. By python find all of its equilibrium points.
2. Calculate the Jacobian matrix at the equilibrium point where x>0 and y>0.
3. Calculate the eigenvalues of the above matrix
4. Determine whether the equilibrium point is stable, unstable, or neutral, and if it is a spriral focus or a neutral center.
