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Unformatted text preview: produced as a function of , and sketch the bifurcation diagrams for all topologically 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 for which formal fast system approximation z x 2 2 y 2 gives incorrect result. R g 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 = v v = g R sin( ) + 2 sin( ) cos( ) (3) Show that a pitchfork bifurcation occurs at a particular value of the parameter . Compute the bifurcation value and draw the bifurcation diagram....
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 Fall '09
 Marsden

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