Consider Xn+1 = f (xn)

Discipline: Accounting

Type of Paper: Question-Answer

Academic Level: Undergrad. (yrs 3-4)

Paper Format: APA

Pages: 1 Words: 275

Question

(1) 4. Consider Xn+1 = f (xn) so if € (0, 3) where f : [0, 1] → [0, 1], x H if x = [1,1] and c € (0,2). cx с — cx (a) Find the fixed points of eq. 1 in terms of parameter c. (4 marks] (b) Investigate whether the fixed points identified in (a) are locally asymptotically stable. [7 marks] (C) Let 1 < c < 2. Show that 0, 14c 1fc2 and are period-two points of eq. 1. [7 marks] (d) For g e C™ let h(x) = g"(x), n E N, be the n-fold composition of g with itself. Show that +' 1+ 1+c in-1 n- 1'(x) = 4 (g"-(x))! (g"-22)....!'(x), 1 d dr where [2 marks] (e) Investigate whether the non-trivial period-two points identified in (c) are locally asymptotically stable. [5 marks]

(1)
4. Consider
Xn+1 = f (xn)
so if € (0, 3)
where f : [0, 1] → [0, 1], x H
if x = [1,1]
and c € (0,2).
cx
с — cx
(a) Find th

Expert Answer

answer starts. In this question, we hasse.\nflxn)\nSex\n= [0,1], x=> [c²cx if x = [1,1]\nif ? € [01]\nI find the fixed points of e