Editing Limit cycle (section)

==Definition==
We consider a two-dimensional dynamical system of the form
<math display="block">x'(t)=V(x(t))</math>
where
<math display="block">V : \R^2 \to \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 \R</math>. An [[orbit (dynamics)|orbit]] is the [[image (mathematics)|image]] of a trajectory, a subset of <math>\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.