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is a smooth function. A trajectory of this system is some smooth function <math>x(t)</math> with values in <math>\mathbb{R}^2</math> which satisfies this differential equation. Such a trajectory is called closed (or periodic) if it is not constant but returns to its starting point, i.e. if there exists some <math>t_0>0</math> such that <math>x(t+t_0)=x(t)</math> for all <math>t\in\mathbb{R}</math>. An orbit is the image of a trajectory, a subset of <math>\mathbb{R}^2</math>. A closed orbit, or cycle, is the image of a closed trajectory. A limit cycle is a cycle which is the limit set of some other trajectory.

is a smooth function. A trajectory of this system is some smooth function <math>x(t)</math> with values in <math>\mathbb{R}^2</math> which satisfies this differential equation. Such a trajectory is called closed (or periodic) if it is not constant but returns to its starting point, i.e. if there exists some <math>t_0>0</math> such that <math>x(t+t_0)=x(t)</math> for all <math>t\in\mathbb{R}</math>. An orbit is the image of a trajectory, a subset of <math>\mathbb{R}^2</math>. A closed orbit, or cycle, is the image of a closed trajectory. A limit cycle is a cycle which is the limit set of some other trajectory.

是一个平滑函数。这个系统的轨迹是满足这个微分方程的光滑函数。如果这个轨迹不是恒定的，而是返回到它的起始点，那么这个轨迹称为闭合(或周期)轨迹。如果存在一些 <math>t_0>0</math>有<math>x(t+t_0)=x(t)</math>对于所有的<math>t\in\mathbb{R}</math>。轨道是轨道的图像，是 < math > mathbb { r } ^ 2 </math > 的子集。一个闭合轨道，或循环，是一个闭合轨迹的图像。极限环是一个循环，它是其他轨迹的极限集。

是一个平滑函数。这个系统的轨迹是满足这个微分方程的光滑函数。如果这个轨迹不是恒定的，而是返回到它的起始点，那么这个轨迹称为闭合(或周期)轨迹。如果存在一些 <math>t_0>0</math>有<math>x(t+t_0)=x(t)</math>对于所有的<math>t\in\mathbb{R}</math>。轨道是轨迹的图像，是<math>mathbb{r}^2</math>的子集。一个闭合轨道，或循环，是一个闭合轨迹的图像。极限环是一个循环，它是其他轨迹的极限集。

 

 

==Properties==

==Properties==