chaos theory - definição. O que é chaos theory. Significado, conceito
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O que (quem) é chaos theory - definição

FIELD OF MATHEMATICS ABOUT DYNAMICAL SYSTEMS HIGHLY SENSITIVE TO INITIAL CONDITIONS
Chaos Theory; Chaotic system; Chaotic systems; The order of choas; Chaotic behavior; Jerk system; Jerk circuit; Chaotic map; Chaotic motion; Chaology; Chaotic dynamical system; Chaos (Mathematics); Classical chaos; Chaos (physics); Disorganized; Deterministic chaos; Deterministic chaotic system; Chaotic dynamical systems; Nonchaotic behavior of quadratic differential systems; Chaotic behavior in systems; Chaos (mathematics); Chaotic orbit; Applications of chaos theory; History of chaos theory; High-dimensional chaos; Chaotic oscillator; Chaotic oscillation; Transition to chaos
  • Soviet physicist]] [[Lev Landau]], who developed the [[Landau-Hopf theory of turbulence]]. [[David Ruelle]] and [[Floris Takens]] later predicted, against Landau, that [[fluid turbulence]] could develop through a [[strange attractor]], a main concept of chaos theory.
  • The red cars and blue cars take turns to move; the red ones only move upwards, and the blue ones move rightwards. Every time, all the cars of the same colour try to move one step if there is no car in front of it. Here, the model has self-organized in a somewhat geometric pattern where there are some traffic jams and some areas where cars can move at top speed.
  • [[Barnsley fern]] created using the [[chaos game]]. Natural forms (ferns, clouds, mountains, etc.) may be recreated through an [[iterated function system]] (IFS).
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  • mod]] 1</span> displays sensitivity to initial x positions. Here, two series of ''x'' and ''y'' values diverge markedly over time from a tiny initial difference.
  • mod]] 1</span> also displays [[topological mixing]]. Here, the blue region is transformed by the dynamics first to the purple region, then to the pink and red regions, and eventually to a cloud of vertical lines scattered across the space.
  • Coexisting chaotic and non-chaotic attractors within the generalized Lorenz model.<ref name=":4" /><ref name=":5" /><ref name=":6" /> There are 128 orbits in different colors, beginning with different initial conditions for dimensionless time between 0.625 and 5 and a heating parameter r = 680. Chaotic orbits recurrently return close to the saddle point at the origin. Nonchaotic orbits eventually approach one of two stable critical points, as shown with large blue dots. Chaotic and nonchaotic orbits occupy different regions of attraction within the phase space.
  • double-rod pendulum]] at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different [[initial condition]] would result in a vastly different [[trajectory]]. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.
  • center
  • Six iterations of a set of states <math>[x,y]</math> passed through the logistic map. The first iterate (blue) is the initial condition, which essentially forms a circle. Animation shows the first to the sixth iteration of the circular initial conditions. It can be seen that ''mixing'' occurs as we progress in iterations. The sixth iteration shows that the points are almost completely scattered in the phase space. Had we progressed further in iterations, the mixing would have been homogeneous and irreversible. The logistic map has equation <math>x_{k+1} = 4  x_k  (1 - x_k )</math>. To expand the state-space of the logistic map into two dimensions, a second state, <math>y</math>, was created as <math>y_{k+1} = x_k + y_k </math>, if <math>x_k + y_k <1</math> and <math>y_{k+1} = x_k + y_k -1</math> otherwise.
  • period-doubling]] as ''r'' increases, eventually producing chaos. Darker points are visited more frequently.
  • ''b'' {{=}} 8/3}}
  • Lorenz equations used to generate plots for the y variable. The initial conditions for ''x'' and ''z'' were kept the same but those for ''y'' were changed between '''1.001''', '''1.0001''' and '''1.00001'''. The values for <math>\rho</math>, <math>\sigma</math> and <math>\beta</math> were '''45.92''', '''16''' and '''4 ''' respectively. As can be seen from the graph, even the slightest difference in initial values causes significant changes after about 12 seconds of evolution in the three cases. This is an example of sensitive dependence on initial conditions.
  • access-date=2013-04-10}}</ref>
  • The [[Lorenz attractor]] displays chaotic behavior. These two plots demonstrate sensitive dependence on initial conditions within the region of phase space occupied by the attractor.

chaos theory         
¦ noun the branch of mathematics that deals with complex systems whose behaviour is highly sensitive to slight changes in conditions, so that small alterations can give rise to strikingly great consequences.
Chaos Theory (disambiguation)         
WIKIMEDIA DISAMBIGUATION PAGE
Chaos Theory (Album); Chaos Theory (album); Chaos theory (disambiguation)
Chaos theory is a mathematical theory describing erratic behavior in certain nonlinear dynamical systems.
chaology         
[ke?'?l?d?i]
¦ noun Physics the study of chaotic systems.
Derivatives
chaologist noun

Wikipédia

Chaos theory

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.

Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and 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. The theory was summarized by Edward Lorenz as:

Chaos: When the present determines the future, but the approximate present does not approximately determine the future.

Chaotic behavior exists in many natural systems, including fluid flow, heartbeat irregularities, weather, and climate. It also occurs spontaneously in some systems with artificial components, such as the road traffic. This behavior can be studied through the analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in a variety of disciplines, including meteorology, anthropology, sociology, environmental science, computer science, engineering, economics, ecology, and pandemic crisis management. The theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, and self-assembly processes.

Exemplos do corpo de texto para chaos theory
1. This leaves us with only the Hollywood/Chaos Theory: More households are drawn to Democratic clambakes because they historically have had more Hollywood star wattage.
2. Advertisement The moralistic school says, however, that what we‘re facing is not merely a giant mess, but rather chaos theory with a particular address.
3. But research suggests that the regulation operates in accord with an algorithm based on mathematical chaos theory, explain Japanese scientists Takanori Ito and Kikukatsu Ito in the November Physical Review E.
4. Ventimiglia says he‘ll appear in the upcoming films "Game" and "The Chaos Theory." "I try and take a break and take a vacation," he says, "but I keep getting wrapped up in jobs." E–mail to a friend
5. "A completely fascinating scientific book about post–chaos theory, which endeavours to explain why simplicity exists at all in a complex world, but is written as engagingly amusingly as a novel." Marina watched Showgirls, again.