Pitchfork bifurcation

Summary

A pitchfork bifurcation is a change in a family of dynamical systems with a symmetry, at which one equilibrium point splits into three. It typically occurs when the system is unchanged under $x \mapsto -x$, so equilibria come in symmetric pairs. In the supercritical case, a stable equilibrium becomes unstable and two new stable equilibria appear on either side. See the definition.