q10-sol - Math 454 Quiz #10 Fall 2008 Sect. 1 Problem....

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Unformatted text preview: Math 454 Quiz #10 Fall 2008 Sect. 1 Problem. Consider the equations where u > 0 is a parameter. (a) Find the eigenvalues of the J acobian at the origin as a function of u. (b) Find the critical value M at which a bifurcation occurs. What kind of bifurcation is it? (c) Sketch the phase portrait at u = MC. -X- ><' w) 3690?): #6 “a O O ~l D) Q) 2 Ha. I O o ,l ) ( : JJ—I) —\ 00"“ mm/(Tx 75 diagonal , (to) 'Bii’immmw 0cm mt 5M3" 4‘21 5L 6%5' N we?“ VOL/177M) H”; W9 {new W 4o 97; NW 4c:on nee/6“ «$962101 75 4'5 :fléatt *- /-~)\'“§+O(XZ)> "=— wow ~x‘ 7’ ©0559 ‘Trovmcmibl Wml agar: 1W9 C(Fhi knew ¢~/fb46‘v\ , ...
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q10-sol - Math 454 Quiz #10 Fall 2008 Sect. 1 Problem....

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