Catastrophes are governed by control parameters whose changes of values leads either to smooth transition at low values or abrupt changes at higher, critical values. Catastrophes indicate points of bifurcation in dynamical systems.
For example, the way a dog can change abruptly from a playful mood to an aggressive stance can be modeled by a simple "catastrophe." In organizations, the presence of sudden change can similarly be modeled using Catastrophe Theory.
In recent years, Catastrophe Theory is understood as a part of Nonlinear Dynamical Systems Theory in general.