he following differential equation contains a parameter, r, which is allowed to vary. x = rx-x² ind all equilibria of this equation in terms of r and determine their stability. Identify any bifurcation values. each: Construct a bifurcation diagram for the equation above, indicating the stability and (approximate) loca- on of all equilibria. Clearly label at least one point on your graph.
he following differential equation contains a parameter, r, which is allowed to vary. x = rx-x² ind all equilibria of this equation in terms of r and determine their stability. Identify any bifurcation values. each: Construct a bifurcation diagram for the equation above, indicating the stability and (approximate) loca- on of all equilibria. Clearly label at least one point on your graph.
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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Transcribed Image Text:The following differential equation contains a parameter, r, which is allowed to vary.
x' = rx-x²
Find all equilibria of this equation in terms of r and determine their stability. Identify any bifurcation values.
Reach: Construct a bifurcation diagram for the equation above, indicating the stability and (approximate) loca-
tion of all equilibria. Clearly label at least one point on your graph.
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