AK-MATH225F10-WS12

AK-MATH225F10-WS12 - MATH225 Fall 2010 Name: \ A...

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Unformatted text preview: MATH225 Fall 2010 Name: \ A Worksheet,12 (10.3, 10.4) Section: Otl 0/3.) For full credit, you must show all work and box answers. ' 1. Consider the system: a = 2$ — y d d—g: = —y + my (a) Find all critical (equilibrium) points. Zx-jz =0 omJ ‘7(:l+X>>“C> ‘0 2 2X20 éfl —)+)<“O x20 X; (b) Using the Jacobian matrix, classify (if possible) é critical (equilibrium) pointfi as a stable node, a stable spiral point, an unstable node, and unstable spiral point, or a saddle point. 2 i X‘\ TAX/7) 27/09)) ;( 7 ~3+><J (0/0): TKO/o) =»( 55 33 "'74 M531 W U310: ZOE)“ “U = Z+Ola>O A: Lona) «(94302) A: H >0 1244A: L4 4940 Wm ( unstuifjpfims Fowl \‘mm-vv-Amwwwlwrln 2. Consider the system: (a) Find all critical (equilibrium) points. 53105010 “WW x2: '35“: 713~I1371"37L)’0 ‘ W) / 6”” o) 7% 5:8 M” w M V“ W” wmfiwmww (b) Using the Jacobian matrix, classify (if possible)’fl critical (equilibrium) pointsas a stable node, a stable sp1ra1 point, an unstable node, and unstable spiral point, or a saddle point. I '3x173yz flax/u u—t tux/7) millx/y) w ( "ax/(7 s—xz—fiyz) 3. Consider the system: (a) Are these species redator- re or competing? X ; Fl"th «tor Tflicfno’ll‘on "far/‘1 (“H‘lei P oaT't'T Vci g, '. P FL. / F” q tarra¢t7tm tcrm ("3/9) (b) What type of growth does species y exhibit in absence f species x? A a, affi/gfl X=of «3-24 fl T'Zyélrrgrl > P7 ( l‘i’B (c) Find all critical (equilibrium) points. z><(—l+273;0 MA 7l1'7“3x>'0 :2 = z. z: » WWW-WW 35: /E: (0/0» (CD/ll] - 2::‘511'2(—3i'3><):© each .,__.___. d Using the Jacobian matrix, classify if possible a, critical equilibrium poin as a stable node a stable s iral 7 P point, an unstable node, and unstable spiral point, or a saddle point. vz+H ‘le 7097); ( ‘37? 7:273X> 2/7297) ' ~2 o . __, 1 a o : LO/o) 1 TKO/O) gz Q Z>:24 (0/er . p) (0/2) (‘9 -1 I4 ’3 : ~'2/+zrro T = Q-Z=U>o l .l a I I _ D Z (2,2 ,T[’7:/2’ “(2% 4: ’A T : *i‘~%40 “LEM: ~‘- 1:40 ) Stable fimel Pol/ft, ...
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AK-MATH225F10-WS12 - MATH225 Fall 2010 Name: \ A...

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