= Structural stability of a bifurcation
A bifurcation is structurally stable within a specified class of systems when every sufficiently small allowed perturbation preserves its local qualitative bifurcation diagram up to smooth changes of state and parameter coordinates. A generic <saddle-node bifurcation> is structurally stable in one-parameter families, whereas a <pitchfork bifurcation> requires a symmetry and a <transcritical bifurcation> requires intersecting equilibrium branches, so unrestricted perturbations destroy either one.
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