BIFURCATIONAL ASPECTS OF CATASTROPHE THEORY

Catastrophe theory, as sketched by Thom, and powerfully developed by Zeeman and others, has aroused some controversy in scientific circles.’-3 It is clear that application of this theory to the social and inexact science, where any mathematical formulation might be suspect, should be pursued with caution. The controversial aspect should not however blind us to the very real insights that this theory can offer in, for example, the physical sciences, particularly in the study of light caustics and elastic Indeed, catastrophe theory is intimately related to theories delineating bifurcation of equilibrium paths of conservative systems. It is the detailed interrelationships between these theories that are explored and illustrated in this paper, with particular emphasis on the crucial topological concept of structural stability. Special attention is given to the imperfection-sensitivity arising in post-buckling of elastic structures. Illustrative examples include the compound instability of stiffened plates and a mechanically stressed atomic lattice.

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