Understanding critical behaviour through visualization: A walk around the pitchfork Original Research Article

Computed 3-dimensional surfaces of critical points, or limit-point shells, are visualized for bifurcation problems that contain a pitchfork as an organizing centre. It is shown by comparison of notionally equivalent problems how the ranges of discontinuous behaviour in nonlinear dynamical models (and the physical systems they purport to represent) are determined by other singularities that shape this surface.