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第36行：
第36行： − 我们考虑一个形式的二维动力系统+ − + − X’(t) = v (x (t)) </math > 第52行：
第51行： − + − 2 to mathbb{r}^2</math>
→Definition
We consider a two-dimensional dynamical system of the form
We consider a two-dimensional dynamical system of the form
我们考虑一个二维动力系统的形式
:<math>x'(t)=V(x(t))</math>
:<math>x'(t)=V(x(t))</math>
<math>x'(t)=V(x(t))</math>
:<math>x'(t)=V(x(t))</math>
where
where
:<math>V:\mathbb{R}^2\to\mathbb{R}^2</math>
:<math>V:\mathbb{R}^2\to\mathbb{R}^2</math>
<math>V:\mathbb{R}^2\to\mathbb{R}^2</math>
：<math>V:\mathbb{R}^2\to\mathbb{R}^2</math>
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 (dynamics)|orbit]] is the [[image (mathematics)|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 (dynamics)|orbit]] is the [[image (mathematics)|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.