Catastrophes {catastrophe theory}| are space discontinuities [Thom, 1968] [Thom, 1972] [Waddington, 1968] [Woodcock and Davis, 1978]. Discontinuity type depends on dimension number. Number of parameters determines how many system states are possible. Actual behavior depends on present state and past history.
transformations
Spaces with four or less dimensions allow seven discontinuous transformations: fold, cusp, swallowtail, butterfly, parabolic umbilic, elliptic umbilic, and hyperbolic umbilic. No other catastrophe types are possible. Discontinuities can appear in continuous-equation systems.
Mathematical Sciences>Computer Science>Systems>Catastrophe Theory
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Date Modified: 2022.0224