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AppDynSys : Hopf Bifurcation : Subcritical
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In the same way that there are supercritical and subcritical pitchfork bifurcations, there are also supercritical and subcritical Hopf bifurcations -- these are rightly viewed as pitchforks in the (nonnegative) radial variable. Illustrated here is a subcritical Hopf, in which an unstable limit cycle annihilates with a stable equilibrium to produce an unstable equilibrium. Danger! These are not nice to meet in the real world...
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