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in relation with the chaos theory......

2007-01-14 03:43:13 · 5 answers · asked by Anonymous in Science & Mathematics Physics

5 answers

Strange attractors first appeared when computers made it possible to simulate dynamical systems, where trajectories of system state was plotted out in configuration space. It was initially expected that either 1) the trajectories would be regular, repeating with clockwork precision, or 2) be completely chaotic with no pattern. What was found was that for some dynamical systems, while the trajectory appeared to be somewhat random, never quite repeating itself, nonetheless seemed to "orbit" about some path in configuration space, so that it was neither 1) or 2). Such paths were called "strange attractors", because the trajectories behaved as if they were being attracted to some path or flow around in configuration space. It was not imagined, however, that there was any real physical force between the two, since this was being conducted entirely in abstract configuration space.

Unlike ordinary coordinate space, which usually have dimensions of length and time, configuration space can make use of any measurable variable in a dynamical system, such as position, angles, momentum, energy, time intervals, etc. They play an important role in Lagrangian and Hamiltonian physics.

2007-01-14 04:05:39 · answer #1 · answered by Scythian1950 7 · 0 0

If you whirl a long piece of string around your head with a small weight on the end, as the weight goes past the same point, imagine it making a 'mark' in the air. Because of the chaotic nature of the way you are whirling the string, each new 'mark' is unlikely to be in exactly the same spot, just close. But if you made enough of these 'marks', they would begin to form a clear shape known as a "strange attractor".

Strange attractors often appear in systems that appear, at first glimpse, to be random and unpredictable; on closer examination, it may turn out that the locations of future data points can be predicted, just not when they will be filled.

2007-01-14 04:26:58 · answer #2 · answered by Anonymous · 0 0

An attractor can be a point, or a manifold, on which a system remains nearby after a long period of time, but not exactly on the attractor. Like a point something oscillates around in the Butterfly diagrams. A strange attractor is a system with a non-integer number of dimensions - it might have 1.3 dimensions, for example.

2007-01-14 03:51:09 · answer #3 · answered by eri 7 · 0 0

an attractor on which the system depends sensitively on the initial conditions. the system moves into the attractor, but its motion on the attractor is chaotic.

2007-01-14 03:49:21 · answer #4 · answered by delujuis 5 · 0 0

The answer is too complex for this forum. Go to wikipedia; I saw an article, but I didn't understand it.

2007-01-14 03:49:26 · answer #5 · answered by Anonymous · 0 0

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