Toronto Math Forum
MAT2442018F => MAT244Tests => Quiz7 => Topic started by: Victor Ivrii on November 30, 2018, 04:11:40 PM

(a) Determine all critical points of the given system of equations.
(b) Find the corresponding linear system near each critical point.
(c) Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system?
(d) Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extend them in those cases where the linear system does not provide definite information about the nonlinear system.
$$\left\{\begin{aligned}
&\frac{dx}{dt} = x  x^2  xy, \\
&\frac{dy}{dt} = 3y  xy  2y^2.
\end{aligned}\right.$$
Bonus: Computer generated picture

Here are my solutions

This is the computer generated picture.

Hi everyone, this is my solution.
For the part(d), I draw the graph by my own method,
just put all single small graphs together.