极限环的表达式和计算

本文提出一种解析法和数值法相结合的方法，用来计算多项式微分系统的极限环，极限环表示为x=∑k≥0(ak cos kφ bk sin kφ),y=∑k≥0(ck cos kφ dk sin kφ)，先用解析法求出小参数时极限环的初始表达式，然后用增量法和迭代法求出任意参数时极限环满足给定精度的表达式，半稳定极限环和分叉值也可以计算。

EXPRESSIONS AND CALCULATION OF LIMIT CYCLES

A method, which is the combination of analytical method and numerical method, is presented for the calculation of limit cycles of polynomial differential systems. The limit cycle is expressed in the form x= Firstly, the initial expressions of the limit cycle in the case of small parameter will be given by using the analytic method. Then the incremental method and the iterative method will be employed to determinate the expressions of the limit cycle with respect to a varying parameter under the desired degree of accuracy. The semi-stable limit cycles and bifurcations can be also calculated.