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6. Consider the 2-dimensional parameter 41-µ2 plane for the differential equation, * + µi ¢ + µz x + x² ¢ + x³ = 0. Show that the system undergoes Hopf bifurcation on the lines Hi = 0 (µ2 > 0) and µi = µ2 (µ2 < 0). (You do Not need to detive the transversal conditions. Hint: Transform the 2nd-order differential equation to a system of 1st-order differential equations.)

6. Consider the 2-dimensional parameter 41-µ2 plane for the differential equation, * + µi ¢ + µz x + x² ¢ + x³ = 0. Show that the system undergoes Hopf bifurcation on the lines Hi = 0 (µ2 > 0) and µi = µ2 (µ2 < 0). (You do Not need to detive the transversal conditions. Hint: Transform the 2nd-order differential equation to a system of 1st-order differential equations.)

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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6. Consider the 2-dimensional parameter 41-µ2 plane for the differential equation, ä + µ1 i + µ2 x + x² ¢ + x³ = 0. Show that the system undergoes Hopf bifurcation on the lines µ1 = 0 (µ2 > 0) and µi = µ2 (42 < 0). (You do Not need to detive the transversal conditions. Hint: Transform the 2nd-order differential equation to a system of 1st-order differential equations.)
Transcribed Image Text:6. Consider the 2-dimensional parameter 41-µ2 plane for the differential equation, ä + µ1 i + µ2 x + x² ¢ + x³ = 0. Show that the system undergoes Hopf bifurcation on the lines µ1 = 0 (µ2 > 0) and µi = µ2 (42 < 0). (You do Not need to detive the transversal conditions. Hint: Transform the 2nd-order differential equation to a system of 1st-order differential equations.)
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