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

作　　者：沈伯骞[1] 刘德明[2] 

机构地区：[1]辽宁师范大学数学系 [2]沈阳师范学院

出　　处：《辽宁师范大学学报（自然科学版）》1990年第2期1-7,共7页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：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

关 键 词：三次曲线解 二次系统 极限环 

分 类 号：O175.12[理学—数学]