dynamical-systems-hw06

# dynamical-systems-hw06 - Step 2 Identify the critical point...

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Instructor: Wayne Hacker Math 550.391-f08 Homework Set 6: ODEs on the real line Grading Scheme for homework problems: Each problem will be graded according to the following scheme: Minor algebra/calculus mistake with a correct approach: 2 out of 3 points given Major algebra/calculus mistake with a correct approach: 1 out of 3 points given Wrong approach: 0 points given The diﬀerences between major and minor mistakes will be determined by the instructor, not the student! This algorithm will be strictly enforced. No exceptions! Diﬃculty Rating Scale: Next to each problem will be the following labels. E = Elementary Level Problem I = Intermediate Level Problem D = Diﬃcult Level Problem The Problems: Section 3.4 Problems : For problems 1-6 do the following steps. Step 1: Find the ﬁxed points.

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Unformatted text preview: Step 2: Identify the critical point ( x c ,r c ). Step 3: Do a local analysis about the critical point ( x c ,r c ) to determine the normal form for the bifurcation. Do not draw the bifurcation diagram. Problem 1: (rating = E) Strogatz 3.4.2 Problem 2: (rating = E) Strogatz 3.4.4 Problem 3: (rating = E) Strogatz 3.4.7 Problem 4: (rating = E) Strogatz 3.4.8 Problem 5: (rating = E) Strogatz 3.4.9 Problem 6: (rating = E) Strogatz 3.4.10 Problem 7: (rating = I) Strogatz 3.4.12 (for the general case only consider n even) Problem 8: (rating = E) Strogatz 3.4.16a Math 550.391, Homework Set 4-f08, Hackernotes c ± Wayne Hacker 2008. All rights reserved. 2 Problem 9: (rating = E) Strogatz 3.4.16b Section 3.5 Problems : Problem 10: (rating = E) Strogatz 3.5.2...
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dynamical-systems-hw06 - Step 2 Identify the critical point...

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