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第231行：
第231行： − + 第237行：
第237行： − 在系统通过极限环状态的周期轨迹中，可能存在一个以上的频率。例如，在物理学中，一个频率可能决定行星绕恒星运行的速率，而另一个频率描述两个天体之间距离的振荡。如果其中两个频率构成一个无理分数(即。它们是不相称的) ，轨迹不再是闭合的，极限环变成了极限环。这种吸引子称为环面，如果存在不相称的频率。例如，这里有一个2-torus:+ + + 第254行：
第256行： − −
→Limit torus
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 极限环===
There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an [[irrational number|irrational fraction]] (i.e. they are [[commensurability (mathematics)|incommensurate]]), the trajectory is no longer closed, and the limit cycle becomes a limit [[torus]]. This kind of attractor is called an {{math|''N''<sub>''t''</sub>}} -torus if there are {{math|N<sub>t</sub>}} incommensurate frequencies. For example, here is a 2-torus:
There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an [[irrational number|irrational fraction]] (i.e. they are [[commensurability (mathematics)|incommensurate]]), the trajectory is no longer closed, and the limit cycle becomes a limit [[torus]]. This kind of attractor is called an {{math|''N''<sub>''t''</sub>}} -torus if there are {{math|N<sub>t</sub>}} incommensurate frequencies. For example, here is a 2-torus:
There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an irrational fraction (i.e. they are incommensurate), the trajectory is no longer closed, and the limit cycle becomes a limit torus. This kind of attractor is called an -torus if there are incommensurate frequencies. For example, here is a 2-torus:
There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an irrational fraction (i.e. they are incommensurate), the trajectory is no longer closed, and the limit cycle becomes a limit torus. This kind of attractor is called an -torus if there are incommensurate frequencies. For example, here is a 2-torus:
在系统通过极限循环状态的周期轨迹中，可能存在多个频率。例如，在物理学中，一个频率可以决定一颗行星围绕恒星运行的速率，而第二个频率则描述了两个天体之间距离的振荡。如果其中两个频率形成[[无理数|无理分数]]（即它们是[[可公度（数学）|不公度]]），则轨迹不再闭合，极限循环变成<font color="#ff8000"> 极限[[环]]</font>。如果存在 {{math|N<sub>t</sub>}}非公度频率，这种吸引子被称为{{math|''N''<sub>''t''</sub>}} 环面。例如，这个2环面体：
与这个吸引子对应的时间序列是一个准周期序列: 具有非公度频率的周期函数(不一定是正弦波)的离散采样和。这样的时间序列不具有严格的周期性，但其功率谱仍然只包含锐线。
与这个吸引子对应的时间序列是一个准周期序列: 具有非公度频率的周期函数(不一定是正弦波)的离散采样和。这样的时间序列不具有严格的周期性，但其功率谱仍然只包含锐线。
=== Strange attractor ===<!-- This section is linked from [[Lorenz attractor]] -->
=== Strange attractor ===<!-- This section is linked from [[Lorenz attractor]] -->