Applications
Chaos theory is applied in many scientific disciplines, including: geology, mathematics, microbiology, biology, computer science, economics, engineering, finance, algorithmic trading meteorology, philosophy, physics, politics, population dynamics, psychology, and robotics.
Chaotic behavior has been observed in the laboratory in a variety of systems, including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices, as well as computer models of chaotic processes. Observations of chaotic behavior in nature include changes in weather, the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. There is some controversy over the existence of chaotic dynamics in plate tectonics and in economics.
Chaos theory is currently being applied to medical studies of epilepsy, specifically to the prediction of seemingly random seizures by observing initial conditions.
Quantum chaos theory studies how the correspondence between quantum mechanics and classical mechanics works in the context of chaotic systems. Relativistic chaos describes chaotic systems under general relativity.
The motion of a system of three or more stars interacting gravitationally (the gravitational N-body problem) is generically chaotic.
In electrical engineering, chaotic systems are used in communications, random number generators, and encryption systems.
In numerical analysis, the Newton-Raphson method of approximating the roots of a function can lead to chaotic iterations if the function has no real roots.
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