# Toronto Math Forum

## MAT244--2018F => MAT244--Tests => Quiz-7 => Topic started by: Victor Ivrii on November 30, 2018, 04:11:40 PM

Title: Q7 TUT 5101
Post 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
Title: Re: Q7 TUT 5101
Post by: Jiabei Bi on November 30, 2018, 04:42:01 PM
Here are my solutions
Title: Re: Q7 TUT 5101
Post by: Ruo Ning Qiu on November 30, 2018, 11:52:30 PM
This is the computer generated picture.
Title: Re: Q7 TUT 5101
Post by: Mengfan Zhu on December 01, 2018, 02:51:46 AM
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.