Mathematical bases of a system where irregular and erratic fluctuations in economic cycles, financial markets, weather, other complex phenomenon, or nonlinear systems with many variables are due to sensitivity to initial changes in values. The theory holds that small changes at the beginning in the starting conditions of the system produces outcomes totally out of proportion to their magnitude. This renders the system inherently unpredictable in the long term. French mathematician Jules Henri Poincarac (1854-1912) layed the groundwork for this system model and theory.