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Consider the difference equation 1-xn xn+1 = = f (xn). 3xn+1 Sketch the curve f(xn) as a function of xn. Determine any fixed points of the difference equation and determine their stability. Finally, determine an expression for xn+2 as a function of xn. Use this map to determine if there are any cycles of period 2, and determine their stability.

Consider the difference equation 1-xn xn+1 = = f (xn). 3xn+1 Sketch the curve f(xn) as a function of xn. Determine any fixed points of the difference equation and determine their stability. Finally, determine an expression for xn+2 as a function of xn. Use this map to determine if there are any cycles of period 2, and determine their stability.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you please show the sketch and the mathematical working out 

Consider the difference equation 1-xn xn+1 = = f (xn). 3xn+1 Sketch the curve f(xn) as a function of xn. Determine any fixed points of the difference equation and determine their stability. Finally, determine an expression for xn+2 as a function of xn. Use this map to determine if there are any cycles of period 2, and determine their stability.
Transcribed Image Text:Consider the difference equation 1-xn xn+1 = = f (xn). 3xn+1 Sketch the curve f(xn) as a function of xn. Determine any fixed points of the difference equation and determine their stability. Finally, determine an expression for xn+2 as a function of xn. Use this map to determine if there are any cycles of period 2, and determine their stability.
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