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Chaos theory
1 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
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Chaos theory Chaotic dynamics
1 In common usage, "chaos" means "a state of disorder". However, in chaos
theory, the term is defined more precisely. Although there is no
universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:
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Chaos theory History
1 An early proponent of chaos theory was Henri Poincaré
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Chaos theory History
1 Despite initial insights in the first half of the twentieth century, chaos theory became
formalized as such only after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at
that time, simply could not explain the observed behaviour of certain experiments like that of the
logistic map. What had been beforehand excluded as measure imprecision and simple
"noise" was considered by chaos theories as a full component of the studied systems.
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Chaos theory History
1 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 visualize these systems.
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Chaos theory History
1 In 1975 Mandelbrot published The Fractal Geometry of Nature, which became a classic
of chaos theory
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Chaos theory History
1 The following year, independently the French Pierre Coullet and Charles Tresser with the
article "Iterations d'endomorphismes et groupe de renormalisation" and the
American Mitchell Feigenbaum with the article "Quantitative Universality for a Class
of Nonlinear Transformations" described logistic maps. They notably discovered the
universality in chaos, permitting an application of chaos theory to many different
phenomena.
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Chaos theory History
1 Then in 1986, the New York Academy of Sciences co-organized with the National
Institute of Mental Health and the Office of Naval Research the first important conference
on Chaos in biology and medicine. There, Bernardo Huberman presented a
mathematical model of the eye tracking disorder among schizophrenics. This led to a renewal of physiology in the 1980s through the application of chaos theory, for example in the study of pathological cardiac cycles.
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Chaos theory History
1 At first the domain of work of a few, isolated individuals, chaos theory
progressively emerged as a transdisciplinary and institutional
discipline, mainly under the name of nonlinear systems analysis
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Chaos theory History
1 The availability of cheaper, more powerful computers broadens the
applicability of chaos theory. Currently, chaos theory continues to
be a very active area of research, involving many different disciplines (mathematics, topology, physics,
social systems, population biology, biology, meteorology, astrophysics, information theory, computational
neuroscience, etc.).https://store.theartofservice.com/the-chaos-theory-toolkit.html
Chaos theory Applications
1 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.
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Chaos theory Applications
1 Chaos theory is currently being applied to medical studies of epilepsy, specifically to the
prediction of seemingly random seizures by observing initial
conditions.
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Chaos theory Applications
1 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.
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Chaos theory Textbooks
1 Kiel, L. Douglas; Elliott, Euel W. (1997). Chaos Theory in the Social
Sciences. Perseus Publishing. ISBN 0-472-08472-0.
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Chaos theory Semitechnical and popular works
1 Abraham, Ralph H.; Ueda, Yoshisuke, eds. (2000). The Chaos Avant-Garde: Memoirs of the Early Days of Chaos Theory. World Scientific. ISBN 978-
981-238-647-2.
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Chaos theory Semitechnical and popular works
1 John Briggs and David Peat, Turbulent Mirror: : An Illustrated Guide to Chaos
Theory and the Science of Wholeness, Harper Perennial 1990,
224 pp.
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Chaos theory Semitechnical and popular works
1 L Douglas Kiel, Euel W Elliott (ed.), Chaos Theory in the Social Sciences:
Foundations and Applications, University of Michigan Press, 1997,
360 pp.
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Complex systems - Complexity and chaos theory
1 Complexity theory is rooted in chaos theory, which in turn has its origins
more than a century ago in the work of the French mathematician Henri
Poincaré
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Complex systems - Complexity and chaos theory
1 When one analyzes complex systems, sensitivity to initial
conditions, for example, is not an issue as important as within the chaos theory in which it prevails
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Complexity science - Complexity and chaos theory
1 Complexity theory is rooted in chaos theory, which in turn has its origins
more than a century ago in the work of the French mathematician Henri
Poincaré
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Complexity science - Complexity and chaos theory
1 When one analyzes complex systems, sensitivity to initial
conditions, for example, is not an issue as important as within the chaos theory in which it prevails
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Chaos theory in organizational development
1 In organizational development, 'chaos theory' is a subset of more
general chaos theory that incorporates principles of quantum mechanics and presents them in a
complex systems environment
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Dynamical systems theory - Chaos theory
1 :Chaos theory describes the behavior of certain dynamical system
(definition)|dynamical systems – that is, systems whose state evolves with
time – that may exhibit dynamics that are highly sensitive to initial
conditions (popularly referred to as the butterfly effect)
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Robert Shaw (physicist) - Chaos theory
1 He was one of the pioneers of Chaos (physics)|chaos theory and his work at
University of California, Santa Cruz on the subject was among the first research into
the relationship between predictable motion and chaos in a landmark PhD
thesis.Robert Shaw, The Dripping Faucet As a Model Chaotic System, Science Frontier Express Series, Aerial Press, December
1984, December 1984 ISBN 0-942344-05-7
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Instructional Simulation - Hermeneutics, fuzzy logic, and chaos theory
1 Chaos theory looks for order in chaotic systems, looking for repeating patterns such
as fractals
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Chaos Theory (disambiguation)
1 * Chaos Theory – Splinter Cell 3
Soundtrack
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Chaos Theory (disambiguation)
1 * Chaos Theory (The Unit)|Chaos Theory (The Unit)
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Splinter Cell - Tom Clancy's Splinter Cell: Chaos Theory (2005)
1 Ubisoft Montreal was again responsible for the third game in the
series, Chaos Theory. It adds a cooperative multiplayer mode.
Originally announced to be released in Fall 2004, its initial releases were
made at the end of March 2005. Again the Unreal Engine was heavily modified, this time from version 2.5.
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Chaos Theory (film)
1 'Chaos Theory' is a 2008 comedy-drama film starring Ryan Reynolds,
Emily Mortimer and Stuart Townsend. The film was directed by Marcos
Siega, written by Daniel Taplitz and Kathy Gori and was shot in
Vancouver|Vancouver, Canada.
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Chaos Theory (film) - Reception
1 Chaos Theory received generally negative reviews from critics on
Rotten Tomatoes and Metacritic. As of July 27, 2011, the review
aggregator Rotten Tomatoes reported that 29% of critics gave the film positive reviews, based on 58
reviews. Metacritic reported the film had an average score of 44 out of
100, based on 18 reviews as of August 2009.
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