{ 62 = wi + sin , cos 62 W2 + sin 62 cos e where wi, w2 > 0. (a) Sketch all the qualitatively different phase portraits

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62 Wi Sin Cos 62 W2 Sin 62 Cos E Where Wi W2 0 A Sketch All The Qualitatively Different Phase Portraits 1 (42.74 KiB) Viewed 32 times

{ 62 = wi + sin , cos 62 W2 + sin 62 cos e where wi, w2 > 0. (a) Sketch all the qualitatively different phase portraits that arise as wi,w2 vary. Hint: Consider a change of variables that leads to decopuled equations. (b) Find the curves in w1,w2 parameter space along which bifurcations occur and classify the various bifurcations. One of these is a global bifurcation we have not discussed in class, a so-called infinite-period bifucation. Explain what this is and why its name is appropriate. (c) Plot the stability diagram in wi,w2 parameter space.