具三次曲线解的二次系统至多有一个极限环  

THE PLANAR QUADRATIC SYSTEM WITH AN INVARIANT CUBIC CURVE HAS AT MOST ONE LIMIT CYCLE

作　　者：水树良[1] 

机构地区：[1]浙江师范大学数理与信息科学学院,金华321004

出　　处：《应用数学学报》2001年第4期590-595,共6页Acta Mathematicae Applicatae Sinica

摘　　要：本文研究具有三次曲线解ｘ３－ｘ２－ｙ２＝０的二次系统，证明此类二次系统最多只有一个极限环，进而证明了具有三次曲线解的二次系统至多有一个极限环．a planar quadratic system with an invariant cubic curve x3-x2-y2=0 is studied. The paper first proves that this system has at most one limit cycle, and then, the conclusion that a planar quadractic system with an invariant cubic curve has at most one limit cycle is obtained.

关 键 词：二次系统 三次曲线解 极限环 唯一性 

分 类 号：O175.1[理学—数学]