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单词 Attraction basin
释义

Attraction basin

中文百科

吸引子 Attractor

(重定向自Attraction basin)
洛伦兹吸引子

吸引子是微积分和系统科学论中的一个概念。一个系统有朝某个稳态发展的趋势,这个稳态就叫做吸引子。吸引子分为平庸吸引子和奇异吸引子。

例如一个钟摆系统,它有一个平庸吸引子,这个吸引子使钟摆系统向停止晃动的稳态发展。

平庸吸引子有不动点(平衡)、极限环(周期运动)和整数维环面(概周期运动)三种模式。而不属于平庸的吸引子的都称为奇异吸引子,它表现了混沌系统中非周期性,无序的系统状态,例如天气系统。


对于吸引子,学术上并没有完善的定义,目前仅处于概念阶段。吸引子中的奇异吸引子对于混沌系统的研究意义重大

英语百科

Attractor 吸引子

(重定向自Attraction basin)
Visual representation of a strange attractor
Attracting period-3 cycle and its immediate basin of attraction for a certain parametrization of f(z) = z2 + c. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.
Weakly attracting fixed point for a complex number evolving according to a complex quadratic polynomial. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.
Van der Pol phase portrait: an attracting limit cycle

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.

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