MAT244--2018F > Quiz-6
Q6 TUT 0601
Victor Ivrii:
The coefficient matrix contains a parameter $\alpha$.
(a) Determine the eigenvalues in terms of $\alpha$.
(b) Find the critical value or values of $\alpha$ where the qualitative nature of the phase portrait for
the system changes.
(c) Draw a phase portrait for a value of $\alpha$ slightly below, and for another value slightly above,
each critical value.
$$\mathbf{x}' =\begin{pmatrix}
0 &-5\\
1 &\alpha
\end{pmatrix}\mathbf{x}.$$
Guanyao Liang:
This is my answer.
Zhiya Lou:
here is my solution
Victor Ivrii:
Zhiya is right but one needs to justify counterclockwise direction of rotation (complex roots) and find directions of eigenvectors (real roots).
Also, what happens as $\alpha =\pm \sqrt{20}$?
Mengfan Zhu:
Hello everyone, this is my answer for quiz 6.
To analyze part(c), I think that we can divide this question into two parts: the real roots and complex roots.
But I am not sure, do we need to consider other conditions?
Is there anyone can share your opinions below?
Thank you very much.
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