dynamical-systems-hw11

# Dynamical-systems-hw - (rating = E Strogatz 7.1.2 Problem 2(rating = E Strogatz 7.1.4 Problem 3(rating = E Strogatz 7.1.5 Problem 4(rating = I

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Instructor: Wayne Hacker Math 550.391-f08 Homework Set 11: 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

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Math 550.391, Homework Set 11-f08, Hackernotes c ± Wayne Hacker 2008. All rights reserved. 2 The Problems: Section 7.1 Problems : Problem 1:
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Unformatted text preview: (rating = E) Strogatz 7.1.2 Problem 2: (rating = E) Strogatz 7.1.4 Problem 3: (rating = E) Strogatz 7.1.5 Problem 4: (rating = I) Strogatz 7.1.8 Section 7.2 Problems : Problem 5: (rating = E) Strogatz 7.2.2 Problem 6: (rating = E) Strogatz 7.2.6(a) Problem 7: (rating = E) Strogatz 7.2.7 (a),(b) (Do not graph phase portrait) Problem 8: (rating = I) Strogatz 7.2.10 Section 7.3 Problems : Problem 9: (rating = I) Consider the dynamical system ( x =-xy 2 (1 + y 3 ) , y = x 2-y 3 . (a) Show that this system is not a gradient dynamics. (b) Show, however, that V = ax n + y m is Lyapunov function for the xed point at the origin with a suitable choice of real a and integer n , m . Conclude that the system has no periodic solutions. Problem 10: (rating = I) Strogatz 7.3.5...
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## This note was uploaded on 02/28/2011 for the course MATH 550.391 taught by Professor Dr.hacker during the Fall '08 term at Johns Hopkins.

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Dynamical-systems-hw - (rating = E Strogatz 7.1.2 Problem 2(rating = E Strogatz 7.1.4 Problem 3(rating = E Strogatz 7.1.5 Problem 4(rating = I

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