在数学中，特别是在动态系统理论里，一个二维平面或二维流形上的的极限环是相空间里的一个闭合的轨迹，使得至少另一个轨迹会随自变量变化而逐渐逼近它（在自变量趋于正无穷或负无穷的时候）。如果当[时间t 时，所有的邻近轨迹都趋近于极限环，那幺所在的流形被称为稳定的，或者称极限环是稳定的（吸引的）。反之，如果 t 时，所有的邻近轨迹都趋近于极限环，那幺称流形是不稳定的或者极限环是不稳定的（非吸引的）。在所有其它情况下，流形既不是稳定也不是不稳定的。

稳定的极限环会导致持续振荡的情况：若一开始轨迹是极限环，则关于轨迹的任意的小扰动都会导致系统重新回到极限环的状态。

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one another trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of a great many real world oscillatory systems. The study of limit cycles was initiated by Henri Poincaré (1854-1912).