Consider the predator prey type of system that's given above with a>0. The population x is prey. By itself, its rate of growth increases for small populations and then decreases for x>1. The predator is given by y, and it dies out when no prey is present. The parameter is given by a. You are asked to show that this system has a Hopf bifurcation.
i) Find the fixed point (xa,ya) with both xa,ya positive.