A population N is controlled by the following discrete difference equation, specified in piecewise-form (i.e. with different expressions for different ranges of N₁): with parameters X>0 and B> 0. The case X = 1 is a special case, so for the purpose of this question, you should assume λ + 1. N*,1 a(i) Find the two fixed points N.,1 and N.,2 (which may be in terms of the parameters A and B). ordered so that N,1 < N,2. sho = Nt+1 = F(N₂) = , N.,2 JANt, N₁ ≤ B AB³/N², N₁>B = a(ii) For N₁,1, identify the range of feasiblity. (You can already assume A> 0 and B > 0, as stated in the question. Any limited parameter range should be in addition to this.) Always feasible O Never feasible O Feasible for a certain parameter range a(iii) For N.,2, identify the range of feasiblity. Always feasible O Never feasible O Feasible for a certain parameter range
A population N is controlled by the following discrete difference equation, specified in piecewise-form (i.e. with different expressions for different ranges of N₁): with parameters X>0 and B> 0. The case X = 1 is a special case, so for the purpose of this question, you should assume λ + 1. N*,1 a(i) Find the two fixed points N.,1 and N.,2 (which may be in terms of the parameters A and B). ordered so that N,1 < N,2. sho = Nt+1 = F(N₂) = , N.,2 JANt, N₁ ≤ B AB³/N², N₁>B = a(ii) For N₁,1, identify the range of feasiblity. (You can already assume A> 0 and B > 0, as stated in the question. Any limited parameter range should be in addition to this.) Always feasible O Never feasible O Feasible for a certain parameter range a(iii) For N.,2, identify the range of feasiblity. Always feasible O Never feasible O Feasible for a certain parameter range
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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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer.
You can borrow
ideas from gpt, but please do not believe its answer.Very very grateful!

Transcribed Image Text:Question 1
A population Nt is controlled by the following discrete difference equation, specified in
piecewise-form (i.e. with different expressions for different ranges of Nt):
with parameters A> 0 and B > 0.
The case X = 1 is a special case, so for the purpose of this question, you should assume λ = 1.
Nt ≤ B
N₁+1 = F(N₂) = { \B³ /N², №₁>B
a(i)
Find the two fixed points N.,1 and N,2 (which may be in terms of the parameters A and B).
These should be ordered so that N,1 < N,2.
N.,2 =
N+,1
=
a(ii)
For N₁,1, identify the range of feasiblity. (You can already assume A> 0 and B > 0, as stated in
the question. Any limited parameter range should be in addition to this.)
Always feasible O Never feasible O Feasible for a certain parameter range
a (iii)
For N₁,2, identify the range of feasiblity.
Always feasible O Never feasible O Feasible for a certain parameter range

Transcribed Image Text:a(iv)
If one or both fixed points are feasible only within a certain parameter range, state this parameter
range below. (If this is not the case, please input NA.)
N1: feasible for
N,2: feasible for
(b)
Give expressions for F'(N₂) for this piecewise function. (These may be functions of A, B and
Nt. In Numbas, N₁ must be entered as N_t.)
F'(Nt)
F'(N₁)
=
=
I
I
for Nt < B
for Nt > B.
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