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Unformatted text preview: Math 221, Winter 2016, Section 202 Page 1 of 3 Quiz IX
March 23, 2017 No books. No notes. No calculators. No electronic devices of any kind. Name Student Number Problem 1. (6+2+2+2 points)
Sketch the phase portrait of the dynamical system n+1 "‘ 5 n 5 ya
4 2 :1: + E
yn+l — 5 n 5 317: in the ﬁrst quadrant, using the diagram on the last page. Draw a representative
collection of trajectories. Make sure you indicate the direction of movement along
the trajectories, and whether the trajectories are straight, or curved, or lines, or
points. Assume the initial state vector satisﬁes 9:0 > 0, and yo > 0. Find conditions on
2:0, yo, that assure that .. ,  ‘ I . \«a s 22
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30mg Mae/Am {S :1) = i?) ,_ X1(:3) (h. EA=9._ " SW“) . W: '1’”
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a} 5" § 4‘. '2 I 30nd 0213va ‘ns (:1) =<:’:> : x1 (’3) (XL EM “WC/‘13 2 WC) . Page 2 of 3 Math 221, Quiz IX Page 3 of 3 allWuhan Eﬁx/Qlkofndp'l‘f
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 Spring '10
 PETERSEN
 ﬁrst quadrant, Dynamical systems theory, initial state vector

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