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1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the stability of all equilibria.

1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the stability of all equilibria.

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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Answer both questions please

(1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the stability of all equilibria.
Transcribed Image Text:(1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the stability of all equilibria.
(2) Find the equilibria of и%3 (1— и)(и? — h) in terms of the bifurcation parameter h. Construct a bifurcation diagram and, on it, indicate the stability of all possible equlibrium solutions for all values of h.
Transcribed Image Text:(2) Find the equilibria of и%3 (1— и)(и? — h) in terms of the bifurcation parameter h. Construct a bifurcation diagram and, on it, indicate the stability of all possible equlibrium solutions for all values of h.
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