overdamping

Consider the set of monic fourth-order real polynomials transformed so that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts of the roots of these polynomials is globally minimized at the Swallowtail singular point of the discriminant surface of the set corresponding to a negative real root of multiplicity four.