Explanation Consider the logistic difference equation x t + 1 = 1 4 x t ( 1 − x t ) with x 0 = 0.2 . The first 20 values of x t are given below: t x t + 1 = 1 4 x t ( 1 − x t ) t x t + 1 = 1 4 x t ( 1 − x t ) 0 0.2 11 0.00000 1 0.04000 12 0.00000 2 0.00960 13 0.00000 3 0.00238 14 0.00000 4 0.00059 15 0.00000 5 0.00015 16 0.00000 6 0.00004 17 0.00000 7 0.00001 18 0.00000 8 0.00000 19 0.00000 9 0.00000 20 0.00000 10 0.00000 The graph of x t for t = 1 , 2 , ... , 20 when x 0 = 0.2 is given below: Now consider the logistic difference equation x t + 1 = 1 4 x t ( 1 − x t ) with x 0 = 0

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 2.1, Problem 53E

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To find: how solution of difference equation changes when initial values slightly changes by comparing theplots ofthe value of xt for t=1,2,...,20 , for the logistic difference equation xt+1=14xt(1−xt) for the values x0=0.2 and x0=0.2001 .

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Chapter 2.1, Problem 52E

Chapter 2.1, Problem 54E

Chapter 2 Solutions

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Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.1 - Prob. 53E Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Prob. 60E Ch. 2.1 - 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Prob. 9CS

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how solution of difference equation changes when initial values slightly changes by comparing theplots ofthe value of x t for t = 1 , 2 , ... , 20 , for the logistic difference equation x t + 1 = 1 4 x t ( 1 − x t ) for the values x 0 = 0.2 and x 0 = 0.2001 .

Solution Summary: The author illustrates how the solution of difference equation changes when initial values slightly change by comparing the plots of xt for t=1,2,...

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To find: how solution of difference equation changes when initial values slightly changes by comparing theplots ofthe value of xt for t=1,2,...,20 , for the logistic difference equation xt+1=14xt(1−xt) for the values x0=0.2 and x0=0.2001 .

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