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Finding limit cycles, in general, is a very difficult problem. The number of limit cycles of a polynomial differential equation in the plane is the main object of the second part of Hilbert's sixteenth problem. It is unknown, for instance, whether there is any system <math>x'=V(x)</math> in the plane where both components of <math>V</math> are quadratic polynomials of the two variables, such that the system has more than 4 limit cycles.
Finding limit cycles, in general, is a very difficult problem. The number of limit cycles of a polynomial differential equation in the plane is the main object of the second part of Hilbert's sixteenth problem. It is unknown, for instance, whether there is any system <math>x'=V(x)</math> in the plane where both components of <math>V</math> are quadratic polynomials of the two variables, such that the system has more than 4 limit cycles.
一般来说，寻找极限环是一个非常困难的问题。平面上一个多项式微分方程的极限环的个数是'''<font color="#ff8000">希尔伯特第十六题 Hilbert's sixteenth problem</font>'''第二部分的主要对象。例如，在平面上是否存在一个系统<math>x'=V(x)</math>，其中<math>V</math>的两个组成部分都是两个变量的二次多项式，因此该系统有多于4个极限环。
一般来说，寻找极限环是一个非常困难的问题。平面上一个多项式微分方程的极限环的个数是'''<font color="#ff8000">希尔伯特第十六题 Hilbert's sixteenth problem</font>'''第二部分的主要对象。例如，在平面上是否存在一个系统<math>x'=V(x)</math>，其中<math>V</math>的两个组成部分都是两个变量的二次多项式，这样的系统有多于4个极限环。
== Applications ==
== Applications ==