Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos.
Chaotic behavior can be observed in many natural systems, such as weather. Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.
Read more about Chaos Theory: Chaotic Dynamics, History, Distinguishing Random From Chaotic Data, Applications, Cultural References
Famous quotes containing the words chaos and/or theory:
“To study history means submitting to chaos and nevertheless retaining faith in order and meaning. It is a very serious task, young man, and possibly a tragic one.”
—Hermann Hesse (1877–1962)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)