A mathematical theory and branch of geometry which demonstrates ways in which a system can undergo sudden large changes as one or more of the variables that control it are continuously changed. I.e., the theory explains change through a succession of sudden catastrophes. A small change in one variable can produce a sudden discontinuity in another. Archaeologists use the theory to show how sudden changes can stem from comparatively small variations. It has been used to explain the dramatic change in settlement patterns and the collapse of Maya and Mycenaean civilizations by comparatively small changes without there being large causes such as invasions or natural disaster.