I am mostly stumped with (c) and (d). You don\'t have to do it for all equilibri

Question

I am mostly stumped with (c) and (d). You don't have to do it for all equilibrium points. Just do it for the equilibrium point (0,3). It must have the pictures of the phase portraits to receive the points. Thank you.

For the competing species population model studied in this section, we showed that the equilibrium point (1,1) is a saddle. Find the linearized system near each of the other equilibrium points. Classify each equilibrium point (as either a source, a sink, a saddle, ...). Sketch the phase portrait of each linearized system. Give a brief description of the phase portrait near each equilibrium point of the nonlinear system.

Explanation / Answer

dx/dt=0 ->2x(1- x/2)-xy=0 --> x=0 or 2-x-y=0 ---> point is (0,2)

dy/dt=0 --> y=0 or 3-y-2x=0 ----> point is (3/2,0)

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