Attractor - Wikipedia
网页Attractors are portions or subsets of the phase space of a dynamical system. Until the 1960s, attractors were thought of as being simple geometric subsets of the phase space, like points, lines, surfaces, and simple regions of three-dimensional space.
2.1 Strange Attractors - The Chaos Hypertextbook
网页Strange attractors are an extension of iteration to two and three dimensions. The most famous of these is the Lorenz attractor — a mathematical experiment in weather prediction that uncovered a surprising link between weather, chaos, and fractals.
Attractor -- from Wolfram MathWorld
网页2024年8月22日 · An attractor is a set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically approach in the course of dynamic evolution.
Lorenz system - Wikipedia
网页The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system.
Strange Attractors
网页In dynamical systems, a 'Strange Attractor' is a type of attractor (a region or shape to which points are 'pulled' as the result of a certain process) that arises in certain non-linear systems and is characterized by its fractal structure.
Lorenz attractor - Encyclopedia of Mathematics
网页2020年6月6日 · The concept of an attractor, that is, an attracting set, often includes only the latter of these two properties; however, both the Lorenz attractor and other practically important attractors have both these properties. The Lorenz attractor first appeared in numerical experiments of E.N. Lorenz [1], who investigated the behaviour of the ...
Lorenz Attractor -- from Wolfram MathWorld
网页The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed temperature difference DeltaT, under gravity g, with buoyancy alpha, thermal diffusivity kappa, and kinematic viscosity nu.
网页1 Introduction to strange attractors. References: Berge et al. [1], Strogatz [2], Abraham and Shaw [3] Thus far, we have studied classical attractors: xed points and limit cycles. In this lecture we begin our study of strange attractors. We emphasize their generic features.
Attractor - Scholarpedia
网页2018年7月5日 · Trapped Attracting Sets. Let \ (T\subset X\) be a compact set such that \ (f (T)\) is contained in the interior of \ (T\ .\) Then the intersection \ (A\) of the nested sequence of sets. \ ( T~\supset~f (T)~\supset~f^ {\circ 2} (T)~\supset~\cdots\) will be called a trapped attractor, with \ (T\) as trapping neighborhood.
网页attractors in dynamical systems provides an important connection between measure theoretic and topological dynamics. There are several definitions of attractors that