a. Consider a simpler version of the competing species model where we do not include overcrowding:

x' = x - xy , y' = y - xy.

Here both x and y are non-negative. First, find all equilibrium points of this system.

b. Compute the Jacobian matrix at each equilibrium point.

c. Determine the types of these equilibria.

d. Determine the nullclines and sketch the regions where the vector field points in different directions.

e. Sketch the phase plane for this system with x, y :: 0.