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Unformatted text preview: produced as a function of μ, ω and sketch the bifurcation diagrams for all topo-logically distinct cases. You will need to compute a suitable approximation to the center manifold and apply the Hopf formula for the coeFcient a in the normal form. ±or this system, show that there is a range of values for δ for which “formal” fast system approximation z ≈ − x 2 − 2 y 2 gives incorrect result. R g ω θ Figure 1: Bead on rotating hoop • Consider the system consisting of a bead on a frictionless rotating hoop as depicted in Figure 1. The equations of motion for the system are ˙ θ = v ˙ v = − g R sin( θ ) + ω 2 sin( θ ) cos( θ ) (3) Show that a pitchfork bifurcation occurs at a particular value of the parameter ω . Compute the bifurcation value and draw the bifurcation diagram....
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- Fall '09
- Bifurcation, Bifurcation theory