(c) In the case R = 9/2, determine the basin of attraction of each equilibrium. (d) Describe the bifurcation that occurs for R = 16/3. Compare the long-term behaviour of typical solutions for the two cases R slightly less than 16/3 and R slightly greater than 16/3.
(c) In the case R = 9/2, determine the basin of attraction of each equilibrium. (d) Describe the bifurcation that occurs for R = 16/3. Compare the long-term behaviour of typical solutions for the two cases R slightly less than 16/3 and R slightly greater than 16/3.
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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C And D needed
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Transcribed Image Text:Consider the discrete-time population model Nt+1 = F(N₂), where
F(N) = RN² (1N)
for R> 0.
(a) What is the maximum value of R for which all solutions remain biologically feasible?
(b) Find the equilibria and the values of R for which they exist.
(c) In the case R = 9/2, determine the basin of attraction of each equilibrium.
(d) Describe the bifurcation that occurs for R = 16/3. Compare the long-term behaviour of
typical solutions for the two cases R slightly less than 16/3 and R slightly greater than
16/3.
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