In mathematics and physics, chaos theory deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions (see butterfly effect). As a result of this sensitivity, the observed behavior of physical systems that exhibit chaos appears to be random, even though the model of the system is 'deterministic' in the sense that it is well defined and contains no random parameters. Examples of such systems include the atmosphere, the solar system, plate tectonics, turbulent fluids, economies, and population growth.
A plot of the trajectory Lorenz system for values r = 28, σ = 10, b = 8/3Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. See the article on chaos for a discussion of the origin of the word in mythology, and other uses. When it is said that chaos theory studies deterministic systems, it is necessary to mention a related field of physics called quantum chaos theory which studies non-deterministic systems following the laws of quantum mechanics.