(4 marks) Three difference equations of the form Pn= f(P-1) are given below. For each graph...

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(4 marks) Three difference equations of the form Pn= f(P-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) (b) Po= 0.8 and Pn= f(Pn-1), where f(x) = = 2 I 2 -0.1. (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? (4 marks) Three difference equations of the form Pn= f(P-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) (b) Po= 0.8 and Pn= f(Pn-1), where f(x) = = 2 I 2 -0.1. (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?

Answer rating: 100% (QA)

The equation in part a is of the form P f P n 1 where f x x 2 The cob web plot for this ... View the full answer