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Attractors
★★★★☆Undergraduate
📖Definition
An attractor is a state or set of states that trajectories converge to over time in a dynamical system. Types include point, periodic orbit, and strange attractors.
📐Formulas
lim_t → ∈fty d(x(t), A) = 0
Convergence to attractor A
\begincases \dotx = σ(y-x) \\ \doty = x(ρ - z) - y \\ \dotz = xy - β z \endcases
Lorenz equations (strange attractor)
✏️Examples
예제 1
Explain difference between point, limit cycle, and strange attractors.
예제 2
What characterizes the Lorenz attractor?
📜History
Discovered by: Edward Lorenz (1963)
Discovered in weather model, Lorenz attractor became iconic in chaos theory.
⚡Applications
Meteorology
Atmospheric models
Neuroscience
Brain activity patterns
Economics
Market dynamics
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