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第210行：
第210行： − + + 第218行：
第219行： − 极限环是一个孤立的连续动力系统的周期轨道。例如摆钟的摆动，以及休息时的心跳。(理想摆的极限环不是极限环吸引子的例子，因为它的轨道不是孤立的: 在理想摆的相空间中，周期轨道的任何一点附近都有另一个点属于不同的周期轨道，所以前一个轨道不吸引)。+ + + − + − −
→Limit cycle
在一个[[离散和连续时间|离散时间]]系统中，<font color="#ff8000"> 吸引子</font>可以以有限数量的点的形式依次访问。每个点都称为[[周期点]]。[[逻辑图]]说明了这一点，根据其特定参数值，对于任何“n”值，可以有由2<sup>''n''</sup>点、3×2<sup>''n''</sup>点等组成的<font color="#ff8000"> 吸引子</font>。
在一个[[离散和连续时间|离散时间]]系统中，<font color="#ff8000"> 吸引子</font>可以以有限数量的点的形式依次访问。每个点都称为[[周期点]]。[[逻辑图]]说明了这一点，根据其特定参数值，对于任何“n”值，可以有由2<sup>''n''</sup>点、3×2<sup>''n''</sup>点等组成的<font color="#ff8000"> 吸引子</font>。
=== Limit cycle ===
=== Limit cycle 极限环===
{{main|Limit cycle}}
{{main|Limit cycle}}
{{main |极限环}}
A [[limit cycle]] is a periodic orbit of a continuous dynamical system that is [[isolated point|isolated]]. Examples include the swings of a [[pendulum clock]], and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).
A [[limit cycle]] is a periodic orbit of a continuous dynamical system that is [[isolated point|isolated]]. Examples include the swings of a [[pendulum clock]], and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).
A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. Examples include the swings of a pendulum clock, and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).
A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. Examples include the swings of a pendulum clock, and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).
[[极限环]]是连续动力系统的周期轨道，它是[[孤立点|孤立]]。例如[[钟摆时钟]]的摆动，以及休息时的心跳。（理想摆的极限环不是极限环吸引子的一个例子，因为它的轨道不是孤立的：在理想摆的相空间中，在一个周期轨道的任何一个点附近都有另一个点属于不同周期轨道，因此前一个轨道不具有吸引力）。
[[File:VanDerPolPhaseSpace.png|center|250px|thumb|<center>[[Van der Pol oscillator|Van der Pol]] [[phase portrait]]: an attracting limit cycle</center>]]
[[File:VanDerPolPhaseSpace.png|center|250px|thumb|<center>[[Van der Pol oscillator|Van der Pol]] [[phase portrait]]: an attracting limit cycle</center>]]
[[文件：VanDerPolPhaseSpace.png|center| 250px |拇指|<center>[[Van der Pol振荡器| Van der Pol]][[相位肖像]]：吸引极限环</center>]]
Van der Pol phase portrait: an attracting limit cycle</center>]]
Van der Pol phase portrait: an attracting limit cycle</center>]]
范德波尔相图: 一个吸引极限环 </center > ]
范德波尔相图: 一个吸引极限环 </center>]]
=== Limit torus ===
=== Limit torus ===