AppDynSys : Hopf Bifurcation : Subcritical

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...