chaos

Definition

Apparently random and unpredictable phenomenon, or the behavior of a complex system, where tiny changes in the starting conditions can lead to very large changes over time. Although in common usage chaos means utter confusion and disorganization, in mathematics it signifies that the equations expressing nonlinear systems are extremely sensitive to initial inputs. And that, while such systems normally show some regularity, it is impossible to predict their future behavior with a high degree of certainty. The term was introduced by the US mathematicians Tien lien Li and James A. Yorke in their 1975 paper 'Period 3 Implies Chaos' which dealt with logistic (differential) functions. The authors, however, did not define 'chaos' and despite its popularity this term (like 'system') remains without a widely-accepted definition. See also chaotic system.