Linear Systems - Phase portraits help

dre

New member
Joined
Sep 21, 2015
Messages
2
I've attached the question below.

(b) Phase portraits and fingerprint identification: Identify all the possible phase portraits of the system below and their corresponding range of values for parameter A and a given fixed constant \(\displaystyle \, \alpha\, >\, 0.\)

. . . . .\(\displaystyle \dfrac{dx}{dt}\, =\, x\, -\, (A\, -\, \alpha)\, y,\). . . . .\(\displaystyle \dfrac{dy}{dt}\, =\, (A\, +\, \alpha)\, x\, +\, y\)


Unsure what the question is asking here and how to begin. Any help would be great. Thanks :)
 

Attachments

  • hww.jpg
    hww.jpg
    35.4 KB · Views: 1
Last edited by a moderator:
(b) Phase portraits and fingerprint identification: Identify all the possible phase portraits of the system below and their corresponding range of values for parameter A and a given fixed constant \(\displaystyle \, \alpha\, >\, 0.\)

. . . . .\(\displaystyle \dfrac{dx}{dt}\, =\, x\, -\, (A\, -\, \alpha)\, y,\). . . . .\(\displaystyle \dfrac{dy}{dt}\, =\, (A\, +\, \alpha)\, x\, +\, y\)


Unsure what the question is asking here and how to begin.
Do you know what "phase portraits" are? Thank you! ;)
 
Do you know what "phase portraits" are? Thank you! ;)
Yes. I know that I have to find the eigen values in order to draw the phase portraits. So far I have found that λ= 1 ± sqrt( α2 - A2 ).
I don't what ranges of values correspond to each phase portrait. Thanks.
 
Top