quiz9-soln - Math 221 Winter 2016 Section 202 Page 1 of 3...

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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 (21):: —)ooasn—>oo Hm) I) (3 mafia ll” PM 3 >¢<Z W ly°<2x0’ (b):rnisfixed,asn—>oo, Ms {3 (m omw’s, \L ”wens Kl 23:2. W (c)$n<0,forlargeenoughn. “”13 i) ((5) U“ “v3 ll. “PM l“! 230)? cf ‘yo>&rb‘ Math 221, Quiz IX Kan _ ‘E'. :8? ‘(k - (I W Tmuékm wad-6x '. va —g_ g Y» . “/c ->\ ?‘ 30mg Mae/Am {S :1) = i?) ,_ X1(:3) (h. EA=9._ " SW“) . W: '1’”- ‘fl‘ 4/: 4% EMYMSPQ 8w X:\ is Hulk?" 451-» = '(52’ "5% A.» C ’3 a} 5" §- 4‘. '2 -I 30nd 0213va ‘ns (:1) =<:’:> -: x1 (’3) (XL EM “WC/‘13 2 WC) . Page 2 of 3 Math 221, Quiz IX Page 3 of 3 all-Wuhan Efix/Qlkofndp'l‘f y ”3+9 1w MM E\~-\ (hdth‘fles “a” (“fig (3.); r+ ' BIIIIIIIIII 8!il!flilll!“‘. 7-!EZIQEEEHIEX$* Gig-ZIIIIIImej 5aafll!liil!%w 4IIIIIIIIII E 3IIIIIIIIII M 2.!!il!!!‘ 1IIIIIIIIII 01‘2345678910 (i) we ‘9th 0'“ SPMCIL» axe 'h'asedtm CMq'sHhS 09 Q Puivd equk MT“ “5 ”is“L °& whi) Jr“ Ma‘w'uw W? 9M4 4» 99M?) "WWW-S +1) 4‘9 “333* ...
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  • Spring '10
  • first quadrant, Dynamical systems theory, initial state vector

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