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Consider the one-dimensional ODE Ủ =ử tu ta where a is a real parameter. Find the (real) fixed points of the system for all possible values of a and determine their stability. Draw a bifurcation diagram indicating the coordinates of the bifurcation point and the stability of the fixed points by means of solid and dashed lines. Give the name of the type of bifurcation.

Consider the one-dimensional ODE Ủ =ử tu ta where a is a real parameter. Find the (real) fixed points of the system for all possible values of a and determine their stability. Draw a bifurcation diagram indicating the coordinates of the bifurcation point and the stability of the fixed points by means of solid and dashed lines. Give the name of the type of bifurcation.

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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Consider the one-dimensional ODE ů = =u²+u+a, where a is a real parameter. Find the (real) fixed points of the system for all possible values of a and determine their stability. Draw a bifurcation diagram indicating the coordinates of the bifurcation point and the stability of the fixed points by means of solid and dashed lines. Give the name of the type of bifurcation.
Transcribed Image Text:Consider the one-dimensional ODE ů = =u²+u+a, where a is a real parameter. Find the (real) fixed points of the system for all possible values of a and determine their stability. Draw a bifurcation diagram indicating the coordinates of the bifurcation point and the stability of the fixed points by means of solid and dashed lines. Give the name of the type of bifurcation.
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