具有三次曲线解的二次系统的极限环的存在性

Existence of Limit Cycle for a Quadratic System with a Quartic Curve Solution

本文证明了具有三次曲线解y^2=ax^3+bx^2+cx+d的二次系统是可以存在极限环的。证明了当且仅当此三次曲线解的图象具有一个孤立点的情形时,才有可能存在极限环,并得出了此系统存在极限环的条件。

This paper proves that for a quadratic system with a quartic curve solutiony^2=ax^3+bx^2+c^x+d there can exist limit cycle.This paper also proves thatthis system can have limit cycle if and only if the figure of this quartic curvesolution possesses a isolated point.We have found out a condition for the existenceof the limit cycle in this system