Chaos theory


Chaos theory is concerned with non-linear systems, the dynamics of which depend extremely sensitively upon the starting conditions. The predictability of such systems is highly restricted, even in cases where the system's development is subject to strict laws or regularities. This is because the smallest fluctuations in the initial conditions can be reinforced exponentially, while the initial conditions themselves can only be determined experimentally with a finite degree of accuracy, so that fundamental limitations are placed upon the predictability of such systems. One speaks of “deterministic chaos”, an expression which conveys the paradoxical fact that processes in such systems appear to the observer to be completely irregular and chaotic, even though they are governed by deterministic laws. Although this has been known to physicists since the beginning of the 20th century, its importance has only become clear in the context of modern meteorology and the computer simulation of weather patterns. The sensitive dependence of chaotic systems upon their initial conditions has become known to the general public in the “butterfly effect”: in principle, the beat of a butterfly's wing can set off a hurricane at another place on the globe.

All dynamic systems with more than two degrees of freedom can display chaotic behaviour. Chaos theory has found applications in very different contexts and disciplines, such as in astronomy (the movement of planets), physics (turbulence), chemistry (the Belousov–Zhabotinsky reaction), biology (prey-and-predator systems, neural networks), meteorology, medicine (cardiology), sociology (traffic flow), economics (finance markets).

The founders of this area of research include, among others, Henri Poincaré, Edward Lorenz, Benoît B. Mandelbrot, Mitchell Feigenbaum und Siegfried Großmann.


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