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.