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Consider the system ẋ=r x-sinx. a) For the case r=0, find and classify all the fixed points, and sketch the vector field. b) Show that when r>1, there is only one fixed point. What kind of fixed point is it? c) As r decreases from ∞to 0 , classify all the bifurcations that occur. d) For 0<r ≪<1, find an approximate formula for values of r at which bifurcations occur. e) Now classify all the bifurcations that occur as r decreases 0 to -∞. f) Plot the bifurcation diagram for -∞<r<∞, and indicate t
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