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Chaos

  • Definition: "Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. So a simple, if slightly imprecise, way of describing chaos is "chaotic systems are distinguished by sensitive dependence on initial conditions and by having evolution through phase space that appears to be quite random." In particular, a chaotic dynamical system is generally characterized by 1. Having a dense collection of points with periodic orbits, 2. Being sensitive to the initial condition of the system (so that initially nearby points can evolve quickly into very different states), a property sometimes known as the butterfly effect, and 3. Being topologically transitive.

    Source: http://mathworld.wolfram.com

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