AnswerPSet_2010_04

AnswerPSet_2010_04 - Answers P-Set Number 4, 18.385j/2.036j...

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Unformatted text preview: Answers P-Set Number 4, 18.385j/2.036j MIT (Fall 2010) Rodolfo R. Rosales (MIT, Math. Dept., room 2-337, Cambridge, MA 02139) November 5, 2010 Course TA: Jan Molacek, MIT, Math. Dept. room 2-331, Cambridge, MA 02139. Email: [email protected] Contents 1 Problem 6.1.13 - Strogatz (Draw a phase portrait). 2 1.1 Problem 6.1.13 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Problem 6.1.13 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Problem 6.5.06 - Strogatz (Epidemic model revisited). 2 2.1 Problem 6.5.06 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Problem 6.5.06 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Problem 07.02.07 - Strogatz (A system both potential and Hamiltonian). 5 3.1 Problem 07.02.07 statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Problem 07.02.07 answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 Problem 07.02.x1 - 385 xtra (Area evolution). 6 4.1 Problem 07.02.x1 statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.2 Problem 07.02.x1 answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 Problem 07.03.11 - Strogatz (Cycle graphs). 9 5.1 Problem 07.03.11 statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2 Problem 07.03.11 answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 Problem 07.05.06 - Strogatz (Biased van der Pol). 12 6.1 Problem 07.05.06 statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6.2 Problem 07.05.06 answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7 Problem 07.06.02 - Strogatz (Calibrating regular perturbation theory). 21 7.1 Problem 07.06.02 statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 7.2 Problem 07.06.02 answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8 Problem 07.06.14 - Strogatz (Computer test of two timing). 22 8.1 Problem 07.06.14 statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.2 Problem 07.06.14 answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1 2 List of Figures 1.1 Problem 6.1.13. Phase plane portrait: 3 closed orbits and single fixed point. . . . 3 2.1 Problem 6.5.06. Kerrmack-McKendrick epidemic model. . . . . . . . . . . . . . . 5 3.1 Problem 07.02.07. A gradient system. . . . . . . . . . . . . . . . . . . . . . . . . 6 5.1 Problem 07.03.11. Globally attracting cycle graph. . . . . . . . . . . . . . . . . . 10 5.2 Problem 07.03.11. Behavior as t → ∞ near a cycle graph. . . . . . . . . . . . . . 12 6.1 Problem 07.05.06. Biased van der Pol ( a 2 > 1.) Nullclines and flow field. . . . . . 14 6.2 Problem 07.05.06. Biased van der Pol ( a 2 < 1.) Nullclines and flow field. . . . . . 15 6.3 Problem 07.05.06. Biased van der Pol ( μ 1); phase portrait. . . . . . . . . . . 18 6.4 Problem 07.05.06. Biased van der Pol (0Problem 07....
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This note was uploaded on 02/28/2011 for the course MATH 18.385j taught by Professor R. during the Fall '10 term at MIT.

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AnswerPSet_2010_04 - Answers P-Set Number 4, 18.385j/2.036j...

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