8. Consider the following model for the populations of two species in competition in a given environment at time t (for instance, lions and hyenas). Here, x(t) represents the number of hundreds of species X at time t, and y(t) represents the number of hundreds of species Y. at dy it Ty (a) Use the framework of #5 to do a phase plane analysis of this system. (b) For each of the initial conditions given below, describe how the sizes of the populations of X and Y change with time and what happens in the long run. i. (0) = 2, y(0) = 0. ii. x(0) = 2, y(0) = 1. iii. x(0) = 1, y(0) = 4. (From the phase plane analysis only, we cannot determine the exact shape of the trajectory. Draw two possibilities on your sketch. Is there more than one possibility for the limiting behavior, i.e., what happens as t - co?)