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3. Consider the following competing species model with logistic growth for both species: of
(1—5::3I_1_:$2_2$y
dy 5 2
_:_ _2 _ dt 32' '9 my (3') Find the nullclines of the system. (ii) Draw an outline of the phase space and estimate the directions of trajectories along the
nullclines and within each region separated by the nullclines. Clearly label your diagram. (iii) Find all the equilibrium points of the system. (iv) Discuss the linear stability at the equilibrium point with :1: > 0 and y > 0.

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