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Consider an autonomous ordinary differential equation for æ(t) of the form da dt f(x; µ), where u is a bifurcation parameter and f(x; u) is a function with no explicit dependence in the independent variablet. Suppose there is a bifurcation point at (ī, ū) = (0,0). Which canonical bifurcation does the following statement describe? • Two critical points for u < 0, one at x= u (unstable) and the other at x = 0 (stable). • Two critical points for u > 0, one at a = µ (stable) and the other at x = 0 (unstable). O Saddle node O Transcritical O Supercritical pitchfork O Subcritical pitchfork

Consider an autonomous ordinary differential equation for æ(t) of the form da dt f(x; µ), where u is a bifurcation parameter and f(x; u) is a function with no explicit dependence in the independent variablet. Suppose there is a bifurcation point at (ī, ū) = (0,0). Which canonical bifurcation does the following statement describe? • Two critical points for u < 0, one at x= u (unstable) and the other at x = 0 (stable). • Two critical points for u > 0, one at a = µ (stable) and the other at x = 0 (unstable). O Saddle node O Transcritical O Supercritical pitchfork O Subcritical pitchfork

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 an autonomous ordinary differential equation for æ(t) of the form da dt f(x; µ), where u is a bifurcation parameter and f(x; u) is a function with no explicit dependence in the independent variablet. Suppose there is a bifurcation point at (ī, ū) = (0,0). Which canonical bifurcation does the following statement describe? • Two critical points for u < 0, one at x= u (unstable) and the other at x = 0 (stable). • Two critical points for u > 0, one at a = µ (stable) and the other at x = 0 (unstable). O Saddle node O Transcritical O Supercritical pitchfork O Subcritical pitchfork
Transcribed Image Text:Consider an autonomous ordinary differential equation for æ(t) of the form da dt f(x; µ), where u is a bifurcation parameter and f(x; u) is a function with no explicit dependence in the independent variablet. Suppose there is a bifurcation point at (ī, ū) = (0,0). Which canonical bifurcation does the following statement describe? • Two critical points for u < 0, one at x= u (unstable) and the other at x = 0 (stable). • Two critical points for u > 0, one at a = µ (stable) and the other at x = 0 (unstable). O Saddle node O Transcritical O Supercritical pitchfork O Subcritical pitchfork
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