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Consider the system below. i = rx + y – x³3 ÿ = -x+ ry – 2y3 This system has a fixed point at (0,0). For that fixed point, a Hopf bifurcation occurs at some value of r. Identify the bifurcation value, showing your mathematical steps.

Consider the system below. i = rx + y – x³3 ÿ = -x+ ry – 2y3 This system has a fixed point at (0,0). For that fixed point, a Hopf bifurcation occurs at some value of r. Identify the bifurcation value, showing your mathematical steps.

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 system below. i = rx +y – x ý = -x + ry – 2y3 This system has a fixed point at (0,0). For that fixed point, a Hopf bifurcation occurs at some value of r. Identify the bifurcation value, showing your mathematical steps.
Transcribed Image Text:Consider the system below. i = rx +y – x ý = -x + ry – 2y3 This system has a fixed point at (0,0). For that fixed point, a Hopf bifurcation occurs at some value of r. Identify the bifurcation value, showing your mathematical steps.
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