Limit cycles

For some vector fields, states may be attracted into a limit cycle. Rather than stabilizing to a point, the state trajectories converge to a loop path in $X$. For example, they may converge to following a circle. This occurs in a wide variety of mechanical systems in which oscillations are possible. Some of the basic issues, along with several interesting examples for $X = {\mathbb{R}}^2$, are covered in [44].