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The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
“Chaos is a fact of life … and a part of dynamical systems theory,” Lin explains to Popular Mechanics in an email. “Some systems are inherently chaotic, while others are not.
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then ...
Chaos theory is sometimes pointed out as a contradiction to Laplace's demon: it describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences. [9]
Atomic systems, e.g. atoms, ions, and molecules, can be treated in terms of the quantum n-body problem. Among classical physical systems, the n -body problem usually refers to a galaxy or to a cluster of galaxies ; planetary systems , such as stars , planets , and their satellites , can also be treated as n -body systems.
The easy experimental implementation of the circuit, combined with the existence of a simple and accurate theoretical model, makes Chua's circuit a useful system to study many fundamental and applied issues of chaos theory. Because of this, it has been object of much study and appears widely referenced in the literature.
The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos". Adaptation to the edge of chaos refers to the idea that many complex adaptive systems (CASs) seem to intuitively evolve toward a regime near the boundary between chaos and order. [19]
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