# hw5 - x = h + rx + x 3-x 5 . (1) (a) Sketch the bifurcation...

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Math 454 Problem Set #5 Fall 2008 Sect. 1 Due Thursday, 10/2, at the beginning of class. Reminder. You are encouraged to work together on homework problems. However, the ﬁnal write- up must be your own. You will be quizzed on some of these problems, so be sure you can do all the problems without help. Read: Sects. 3.7, 4.0-4.3 Problems - Sect. 3.6 #2(a,b), 3, 4 (*) , 7 - Sect. 3.7 #3: do only (b-d), assuming the equation in (a) - Sect. 4.1 #3, 4, 5 - Sect. 4.3 #1 P1 (Perturbing the subcritical pitchfork.) Consider the vector ﬁeld
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Unformatted text preview: x = h + rx + x 3-x 5 . (1) (a) Sketch the bifurcation diagram when h = 0 . Be sure to label each branch as stable or unstable. (We already did this in class.) (b) Sketch the bifurcation diagrams for h &gt; and h &lt; . Could you have guessed this from looking at the diagram in (a)? (*) Think about what happens if we perturb the saddle-node normal form. That is, how does the bifurcation diagram change if h = 0 in x = r + hx-x 2 ? (2)...
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