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3. Three difference equations of the form Pn= f(Pn-1) are given below. For each graph y = f(x) and y = x, draw a cobweb plot, and use that cobweb plot to analyse the long-term behaviour of each difference equation. 2 = NISNISN (a) Po= 0.8 and Pn = f(Pn-1), where f(x) (b) Po= 0.8 and Pn = f(Pn-1), where f(x): (c) Po= 0.8 and Pn= f(Pn-1), where f(x) = +0.1. Are there windows of periodic behaviour within chaotic regimes in case the long-term behaviour is chaotic for any of these equations? What periodicity do they have? 2 0.1.

3. Three difference equations of the form Pn= f(Pn-1) are given below. For each graph y = f(x) and y = x, draw a cobweb plot, and use that cobweb plot to analyse the long-term behaviour of each difference equation. 2 = NISNISN (a) Po= 0.8 and Pn = f(Pn-1), where f(x) (b) Po= 0.8 and Pn = f(Pn-1), where f(x): (c) Po= 0.8 and Pn= f(Pn-1), where f(x) = +0.1. Are there windows of periodic behaviour within chaotic regimes in case the long-term behaviour is chaotic for any of these equations? What periodicity do they have? 2 0.1.

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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3. Three difference equations of the form Pn = f(Pn-1) are given below. For each graph y = f(x) and y = x, draw a cobweb plot, and use that cobweb plot to analyse the long-term behaviour of each difference equation. (a) Po= 0.8 and Pn = f(Pn-1), where f(x) = NIS 2 2 (b) Po= 0.8 and Pn = f(Pn-1), where f(x) = - X 2 == (c) Po= 0.8 and Pn = f(Pn-1), where f(x) = 0.1. +0.1. X Are there windows of periodic behaviour within chaotic regimes in case the long-term behaviour is chaotic for any of these equations? What periodicity do they have?
Transcribed Image Text:3. Three difference equations of the form Pn = f(Pn-1) are given below. For each graph y = f(x) and y = x, draw a cobweb plot, and use that cobweb plot to analyse the long-term behaviour of each difference equation. (a) Po= 0.8 and Pn = f(Pn-1), where f(x) = NIS 2 2 (b) Po= 0.8 and Pn = f(Pn-1), where f(x) = - X 2 == (c) Po= 0.8 and Pn = f(Pn-1), where f(x) = 0.1. +0.1. X Are there windows of periodic behaviour within chaotic regimes in case the long-term behaviour is chaotic for any of these equations? What periodicity do they have?
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