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d²r 5. For the Van de Pol equation, - p(x² – 1)4+x=0 the parameter u is positve. What if u were negative, for example µ = -1. What do you expect would happen (brief description)? Use your intuitida about 2nd order ODE and oscillators, classify the sole equilibrium point at (r. x'): (0,0), and sketch a phase-portrait for this equation with u=-1 to support your answer. (Bonus: is µ = 0 a bifurcation value? Why or why not?) %3D %3D

d²r 5. For the Van de Pol equation, - p(x² – 1)4+x=0 the parameter u is positve. What if u were negative, for example µ = -1. What do you expect would happen (brief description)? Use your intuitida about 2nd order ODE and oscillators, classify the sole equilibrium point at (r. x'): (0,0), and sketch a phase-portrait for this equation with u=-1 to support your answer. (Bonus: is µ = 0 a bifurcation value? Why or why not?) %3D %3D

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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5. For the Van de Pol equation, (x - 1) +x =0 the parameter u is positve. What if u were negative, for example u = -1. What do you expect would happen (brief description)? Use your intuitida about 2nd order ODE and oscillators, classify the sole equilibrium point at (r, x') = (0,0), and sketch a phase-portrait for this equation with =-1 to support your answer. (Bonus: is = (0 a bifurcation value? Why or why not?). d²r
Transcribed Image Text:5. For the Van de Pol equation, (x - 1) +x =0 the parameter u is positve. What if u were negative, for example u = -1. What do you expect would happen (brief description)? Use your intuitida about 2nd order ODE and oscillators, classify the sole equilibrium point at (r, x') = (0,0), and sketch a phase-portrait for this equation with =-1 to support your answer. (Bonus: is = (0 a bifurcation value? Why or why not?). d²r
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