Question

How to draw phase portrait of
\(x'=x(1-x)-xy\\y'=y((3/4)-y)-(1/2)xy\)
Please, help

Answer 1

This can help you,

http://tutorial.math.lamar.edu/Classes/DE/PhasePlane.aspx

Answer 2

I got equilibrium points as
(0,0) source
(1/2,1/2) sink
(0,3/4) saddle
(1,0) saddle
But don't know how to draw a phase portrait

Answer 3

by hand

Answer 4

In the example 1 of the link, you have a problem where the solution says how to draw it for some vectors (obtain points and vectors). If you do that for a large number of points, then you obtain the phase graph there.

Answer 5

Thanks for the link. But we don't have so many points to manipulate.

Answer 6

Moreover, I have to draw based on equilibrium points only, not eigenvalues, eigenvectors.