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Unformatted text preview: MTH 487-587 ASSIGNMENT 1: ONE DIMENSIONAL FIXED POINTS, STABILITY AND SOLVING DIFFERENTIAL EQUATIONS Information. Write your solutions to the problems below on one side of your paper only . Your work must be neat. For Maple work, provide printouts. Use Ctrl-T and Ctrl-R to put text and math in Maple worksheets explaining what you are doing . For this assignment, as for all others, you may discuss the problems from a general viewpoint with others, but you must write your solutions yourself . This will be strictly enforced. Problem 1 (20 points). Find and classify (i.e. stable or unstable) the fixed points of x = x 3- 6 x 2- 13 x + 42 using a one-dimensional analysis; a two-dimensional Maple analysis. That is, plot the solutions on the plane with different initial values; linear stability analysis (i.e. find f ( x )); and a Liapunov function. (Hint: Maple has a factor command which will help to find fixed points). Problem 2 (20 points). (Strogatz 2.7.2,3,5) For the following, find fixed points and classify them by (1) finding a Liapunov function V ( x ) and relating its properties to the original system as in section 2.7; (2) using linear stability analysis (i.e. find f ( x ))....
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