In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. This may lead to sudden and dramatic changes, for example the unpredictable timing and magnitude of a landslide.
Catastrophe theory originated with the work of the French mathematician René Thom in the 1960s, and became very popular due to the efforts of Christopher Zeeman in the 1970s. It considers the special case where the long-run stable equilibrium can be identified as the minimum of a smooth, well-defined potential function (Lyapunov function).
Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system. However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures.
Any large and disastrous event of great significance.
A disaster beyond expectations
The dramatic event that initiates the resolution of the plot; the dénouement.
A type of bifurcation, where a system shifts between two stable states.
misspelling of catastrophe
An event producing a subversion of the order or system of things; a final event, usually of a calamitous or disastrous nature; hence, sudden calamity; great misfortune.
The final event in a romance or a dramatic piece; a denouement, as a death in a tragedy, or a marriage in a comedy.
A violent and widely extended change in the surface of the earth, as, an elevation or subsidence of some part of it, effected by internal causes.
an event resulting in great loss and misfortune;
"the whole city was affected by the irremediable calamity"
"the earthquake was a disaster"
a state of extreme (usually irremediable) ruin and misfortune;
"lack of funds has resulted in a catastrophe for our school system"
"his policies were a disaster"
a sudden violent change in the earth's surface