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Topic: Chaos theory


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  Chaos Theory- Crystalinks
Thus chaos theory is, very generally, the study of forever changing complex systems based on mathematical concepts of recursion, whether in the form of a recursive process or a set of differential equations modeling a physical system.
Chaos theory attempts to explain the fact that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions.
Chaos theory progressed more rapidly 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 behavior of certain experiments like that of the logistic map.
www.crystalinks.com /chaos.html   (2064 words)

  
 Chaos Homepage
Andrew Ho Chaos theory is among the youngest of the sciences, and has rocketed from its obscure roots in the seventies to become one of the most fascinating fields in existence.
Chaos theory predicts that complex nonlinear systems are inherently unpredictable--but, at the same time, chaos theory also insures that often, the way to express such an unpredictable system lies not in exact equations, but in representations of the behavior of a system--in plots of strange attractors or in fractals.
Chaos theory is great as a way of looking at events which happen in the world differently from the more traditional strictly deterministic view which has dominated science from Newtonian times.
twm.co.nz /chaos_intro.html   (967 words)

  
 Chaos Theory: A Brief Introduction | IMHO
The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.
The bifurcation diagram of the population equation is fractal.
Chaos theory has changed the direction of science: in the eyes of the general public, physics is no longer simply the study of subatomic particles in a billion-dollar particle accelerator, but the study of chaotic systems and how they work.
www.imho.com /grae/chaos/chaos.html   (2929 words)

  
 Chaos Theory and Fractals
Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act.
Chaos refers to the issue of whether or not it is possible to make accurate long-term predictions of any system if the initial conditions are known to an accurate degree.
Chaos is also found in systems as complex as electric circuits, measles outbreaks, lasers, clashing gears, heart rhythms, electrical brain activity, circadian rhythms, fluids, animal populations, and chemical reactions, and in systems as simple as the pendulum.
www.tnellen.com /alt/chaos.html   (1990 words)

  
 Chaos theory
The idea of deterministic chaos did not come to full fruition until after the advent of the computer, which could be used to model systems which were previously unapproachable by traditional methods.
Chaos theory is often illustrated with fractals, geometric constructions that begin as simple elements, but wind up having so many variables that each individual progression seems to be random, yet in the end they do form a clear, repeating pattern.
"Chaos theory" was a term invented by the popular press to describe the part of dynamics usually referred to as Chaos.
everything2.com /index.pl?node_id=39176&displaytype=printable   (3874 words)

  
 Chaos Theory
In recent years, the advent of chaos theory is one of the indications that something is beginning to change in the scientific community.
The birth of chaos mathematics, therefore, is a proof as Engels would have said, of the dialectical character of nature, a reminder that reality consists of whole dynamic systems, or even one whole system, and not of models (however useful) abstracted from them.
The starting point of the supporters of chaos theory was a reaction against precisely this method, which they call "reductionism." Engels explained that the "reduction" of the study of nature to separate disciplines is to some extent necessary and inevitable.
www.marxist.com /science/chaostheory.html   (3138 words)

  
 Chaos Theory (Lorenz Poincaré)
The Chaos Theory method from Lorenz and Poincaré is a technique that can be used for studying complex and dynamic systems to reveal patterns of order (non-chaos) out of seemingly chaotic behaviors.
The theory also has been applied to business cycles, and dynamics of animal populations, as well as in fluid motion, planetary orbits, electrical currents in semi-conductors, medical conditions (like epileptic seizures), and the modeling of arms races.
Chaos theory is not as simplistic to find an immediate and direct application in the business environment, but mapping of the business environment using the knowledge of chaos definitely is worthwhile studying.
www.12manage.com /methods_lorenz_chaos_theory.html   (1369 words)

  
 Whatever Happened to... Chaos Theory? | Math | DISCOVER Magazine
Chaos theory, the study of how tiny fluctuations can have tremendous effects within a moving system, emerged in mainstream physics about 30 years ago.
Chaos theory, or nonlinear dynamics, is a mathematical way of determining the effects of small changes on systems so complex they look random.
The applications of chaos theory touch almost every field, and trying to group them under one umbrella would be a useless and herculean task.
discovermagazine.com /2007/apr/whatever-happened-to-chaos-theory   (502 words)

  
 chaos
Chaos theory began as a field of physics and mathematics dealing with the structures of turbulence and the self-similar forms of fractal geometry.
Attractors in chaos theory are like the influence of gravity, sets of values in the "phase space" to which a system migrates over time, also called islands of stability (possible states of a dynamical system).
The appeal of chaos theory is the view that organizations are complex adaptive systems that have behaviors similar to those found in nature--different stages of stability and chaos.
iit.ches.ua.edu /systems/chaos.html   (3148 words)

  
 Chaos Theory at Polytechnic School
Chaos theory is very much a 20th century development, but the man who probably best deserves the title "Father of Chaos Theory" was a great French mathematician of the 19th century named Henri Poincaré;.
Prediction becomes impossible." This is the statement which gives Poincare the claim to the title "Father of Chaos Theory." This is the first known published statement of the property now known as "sensitivity to initial conditions", which is one of the defining properties of a chaotic dynamical system.
Thus Poincare's monumental discovery of what we now call deterministic chaos was destined to be conveniently placed on the scientific back burner for the next seven decades before being rediscovered by a mathematically trained meteorolgist at the Massachusetts Institute of Technology.
home.earthlink.net /~srrobin/chaos.html   (909 words)

  
 [No title]
Chaos theory is one of a set of approaches to study nonlinear phenomena.
This is an umbrella term for the study of phenomena such as attractors, bifurcations, chaos, fractals, catastrophes, and self-organization, all of which describe systems as they change over time, and there is a large variety of patterns by which change can occur.
It would be correct to call chaos theory in psychology a new paradigm in psychological thought: Nonlinear theory introduces new concepts to psychology for understanding change, new questions that can be asked, and offers new explanations for phenomena.
www.societyforchaostheory.org /tutorials   (2390 words)

  
 Chaos Theory for Beginners; An Introduction
Examples of these complex systems that Chaos Theory helped fathom are earth's weather system, the behavior of water boiling on a stove, migratory patterns of birds, or the spread of vegetation across a continent.
Chaos is everywhere, from nature's most intimate considerations to art of any kind.
Chaos Theory however taught us that nature most often works in patterns, which are caused by the sum of many tiny pulses.
www.abarim-publications.com /ChaosTheoryIntroduction.html   (1516 words)

  
 What is chaos theory? - a definition from WhatIs.com - see also: butterfly effect
chaos theory: In a scientific context, the word chaos has a slightly different meaning than it does in its general usage as a state of confusion, lacking any order.
The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying order, and that very simple or small systems and events can cause very complex behaviors or events.
Although chaos is often thought to refer to randomness and lack of order, it is more accurate to think of it as an apparent randomness that results from complex systems and interactions among systems.
whatis.techtarget.com /definition/0,,sid9_gci759332,00.html   (855 words)

  
 Chaos
Chaos is qualitative in that it seeks to know the general character of a system's long-term behavior, rather than seeking numerical predictions about a future state.
Edward Lorenz would stretch the definition of chaos to include phenomena that are slightly random, provided that their much greater apparent randomness is not a by-product of their slight true randomness.
In Chaos parlance, this is referred to as sensitive dependence on initial conditions.
www.exploratorium.edu /complexity/lexicon/chaos.html   (475 words)

  
 Pi: Chaos Theory
Discovered by a meteorologist in 1960, chaos theory contends that complex and unpredictable results will occur in systems that are sensitive to small changes in their initial conditions.
Apart from the stock market, Chaos Theory can be used to model other highly complex systems, including everything from population growth to epidemics to arrhythmic heart palpitations.
When applying chaos theory, it is revealed that even something as seemingly random as a dripping faucet has an order behind it.
www.pithemovie.com /chaos.html   (239 words)

  
 Chaos Theory - Advanced Topics in Mathematics at CCHS
Chaos Theory is a branch of mathematics that deals with systems that appear to be orderly (deterministic) but, in fact, harbor chaotic behaviors.
Chaos Theory and Mathematics are directly connected with each other.
Although people often think of Chaos theory as connected with weather events and scientific research, mathematicians are heavily involved in studying Chaos Theory as it applies to mathematical functions.
mail.colonial.net /~abeckwith/chaos.html   (983 words)

  
 Chaos and Art - Chaos Theory
One of the main characteristics of chaos is sensitivity to initial conditions.
Although extreme sensitivity to initial conditions alone does not necessarily lead to chaos, it is a very important feature of chaos, for it is the factor that makes long-term predictions meaningless.
If you are interested in chaos theory, but hate reading (who are you?), I highly recommend Darren Aronofsky's Pi (1997), a psychological thriller about faith in chaos.
www.jessiegietl.com /theorypage.html   (671 words)

  
 Chaos Theory
Chaos is often thought of as utter confusion, pandemonium, havoc, or disarray.
The idea of obtaining “order” out of “chaos” may sound like an oxymoron, but its experimental demonstration is so profound that this must rank as one of the most disturbingly fundamental discoveries of modern science.
From this, it should become readily obvious that Chaos Theory is of fundamental importance to life.
www.halexandria.org /dward165.htm   (2989 words)

  
  Splinter Cell Chaos Theory Xbox Game, Splinter Cell Chaos Theory
Behind the scenes of Chaos Theory's co-op mode.
A major fan of the genre and series, i knew that chaos theory was gonna be the big one.
Chaos Theory is, on all levels, an improvement over its predecessors.
www.breakfastpills.1up.com /do/gameOverview?cId=3133414   (482 words)

  
  Chaos theory - Wikipedia, the free encyclopedia
The first discoverer of chaos can plausibly be argued to be Jacques Hadamard, who in 1898 published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature.
Chaos theory progressed more rapidly 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 behavior of certain experiments like that of the logistic map.
The term chaos as used in mathematics was coined by the applied mathematician James A. Yorke.
en.wikipedia.org /wiki/Chaos_theory   (2078 words)

  
 Ionasphere's Chaos Theory Intro
The language of CDS and Chaos Theory is now revealing a point-of-view, or metamodel, which provides a universal language for psychology which is competent to deal with the complexities of interactive change and yet is relatively easy to communicate.
Chaos theory is still very much in its infancy but it is sweeping throughout the scientific world, rapidly finding application not only in hard sciences, such as physics and chemical engineering, but also in economics, psychology, biology, astronomy, demographics, business management,.
Chaos theory implies a universe of evolution and constant re-creation.
www.geocities.com /iona_m/ChaosTheory/CTintro.html   (6417 words)

  
 Chaos FAQ   (Site not responding. Last check: )
Chaos theory is a further development of dynamical systems theory which focusses on highly complex motions called chaotic motions.
Sadly, no. While a small number ofuniversities offer a course in chaos theory in their physics or math departments, there are compreensive chaos theory programs taught be experts in the field only at a handfull of universities.
As chaos theory is a new branch of math, it is relatively independent of the main topics of the trditional progrtam.
www.vismath.org /faq/chaosfaq.html   (619 words)

  
 Chaos Theory   (Site not responding. Last check: )
Chaos theory is once and awhile at risk of being overtaxed by being associated with everything that can be even superficially related to the concept of chaos (9).
In other words, one of the lessons coming out of chaos theory is that the soundness of the causality principle is narrowed by the uncertainty principle from one end as well as by the inherent properties of fundamental natural laws from the other end (12).
Chaos theory is the mathematics of studying such non-linear, dynamic systems.
www.emayzine.com /infoage/math/math1.htm   (13247 words)

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