Chaos

Chaos theory is used to model the overall behavior of complex systems. Despite its name, chaos theory is used to identify order in complex and otherwise seemingly unpredictable systems.

Chaos theory is used to understand explosions, complex chemical reactions (e.g., the Belousov-Zhabotinsky oscillating reaction that yields a red solution that turns blue at varying intervals of time), and many biological and biochemical systems. Chaos theory is now an important tool in the study of population trends and in helping to model the spread of disease. Epidemiologists use chaos theory to help predict the spread of epidemics.

Deterministic dynamical systems are those systems that are predictable based on accurate knowledge of the conditions of the system at any given time. When systems are, however, sensitive to their initial conditions they eventually become unpredictable. In particular, chaos theory deals with complex nonlinear dynamic (i.e., nonconstant, nonperiodic, etc.) systems. Nonlinear systems are those described by mathematical recursion and higher algorithms. Deterministic chaos, is mainly devoted to the study of systems the behavior of which can, in principle, be calculated exactly from equations of motion.

Chaos theory is the study of non-linear dynamic systems, that is, systems of activities (weather, turbulence in fluids, the stock market) that cannot be visualized in a graph with a straight line. Although dictionaries usually define "chaos" as "complete confusion," scientists who study chaos have discovered deep patterns that predict global stability in dynamic systems in spite of local instabilities.