hw10 - ECE320 Homework 10 Cornell University Spring 2006...

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ECE320 Homework 10 Spring 2006 Cornell University T.L.Fine Please hand in this assignment at the end of lecture on Tuesday, 18 April. Use only your assigned three-digit code and not your name. Throughout, give reasons for your answers. 1. (a) Using graphical means for a = 1 + 8, and considering the thrice iter- ated logistic ( logistic ( logistic ( x ))), determine approximately the fixed points of period 3 of the logistic iteration. Submit your graph. (b) Which of these fixed points are of period 1? (c) Select a = 3 . 8285 in the logistic to display period 3 behavior and calculate the first 500 terms. Using the Matlab command hist to help you analyze this data (submit this), can you verify that this sequence eventually approximately achieves the fixed points calculated in (a)? 2. Consider the linear difference equation x n +2 = 2 3 x n +1 + 1 3 x n , with initial state s 2 = ( x 2 , x 1 ) = (1 , - 1 / 2). (a) Does this difference equation system have one or more fixed points?
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