A bifurcation at which an attracting period-n cycle becomes repelling and give birth to an attracting 2n-cycle is a period-doubling bifurcation. The bifurcations of {Qm} are period-doubling bifurcations. Because the graph resembles a pitchfork near the point on the orbit diagram corresponding to the bifurcation, this kind of bifurcation is often called a pitchfork bifurcation.

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