quiz2 - CMPE 8 NAME: Fall 2008 Quiz 2 Quiz Time: 12:0512:45...

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Unformatted text preview: CMPE 8 NAME: Fall 2008 Quiz 2 Quiz Time: 12:0512:45 PM 1. For the dynamic model x k +1 = x k + 1 10 ( 8- x 3 k ) (a) (5 points) Calculate the fixed point(s) x * . First substitute x * in for x k and x k +1 : x * = x * + 1 10 ( 8- x 3 * ) Now, solve for x * : 0 = 1 10 ( 8- x 3 * ) = x 3 * = 8 = x * = 2 So, x * = 2 is the only fixed point. (b) (6 points) Use a calculator and compute the first 6 elements for two different orbits: one starting from x 1 = 0, and the other starting from x 1 = 4 . So, your answer should be two vectors, each with 6 elements. vector 1: (0, 0.8, 1.55, 1.98, 2.00, 2.00) vector 2: (4, -1.6, -0.39, 0.42, 1.21, 1.83) (c) (4 points) Based on the orbits calculated, make a judgment about whether the fixed point(s) are stable, stable and attractive, or unstable. Justify your choice. Both orbits appear to converge back to the fixed point x * = 2, suggesting that this fixed point is stable and attractive....
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quiz2 - CMPE 8 NAME: Fall 2008 Quiz 2 Quiz Time: 12:0512:45...

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