### Author Topic: Q6 TUT 0101  (Read 2130 times)

#### Victor Ivrii

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##### Q6 TUT 0101
« on: November 17, 2018, 03:49:22 PM »
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.
$$\mathbf{x}' =\begin{pmatrix} \frac{5}{4} &\frac{3}{4}\\ \alpha & \frac{5}{4} \end{pmatrix}\mathbf{x}.$$
« Last Edit: November 17, 2018, 04:02:05 PM by Victor Ivrii »

#### Qing Zong

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##### Re: Q6 TUT 0101
« Reply #1 on: November 17, 2018, 04:55:24 PM »
This is my solution

#### Jiacheng Ge

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##### Re: Q6 TUT 0101
« Reply #2 on: November 18, 2018, 12:57:01 PM »
« Last Edit: November 18, 2018, 01:04:09 PM by Jiacheng Ge »

#### Victor Ivrii

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##### Re: Q6 TUT 0101
« Reply #3 on: November 25, 2018, 09:45:15 AM »
Both solutions are barely readable (one due to poor handwriting, second due to making crappy snapshot instead of scanning). The second is complete, but one should explain how "it is different".