摘要
本文研究一类以三次曲线ｘｙ２＋２ｙ－１＝０为不变集的二次系统，除去明显不存在极限的情形外，该二次系统可化为ｄｘｄｔ＝（α－１）－（１＋β）ｘ－βｘ２＋αｘｙｄｙｄｔ＝－β２＋（β＋１２）ｙ＋β２ｘｙ－１＋α２ｙ２经一系列变换，将上述方程化为广义Ｌｉéｎａｒｄ方程，证明此方程最多只有一个极限环，从而完整地解决了此类二次系统的极限环的个数问题。
In this paper,the author considers a quadratic system with an invariant cubic curve\ xy 2+2y-1=0 .The system can be transformed to: d x d t=(α-1)-(1+β)x-βx 2+αxy d y d t=-β2+(β+12)y+β2xy-1+α2y 2 By some transformations,the system can be changed into a generalized Liénard equation,then prove that the equation has at most one limit cycle.Hence give a satisfactory solution to the question of the number of limit cycle of the discussed system.
出处
《浙江师大学报（自然科学版）》
1999年第1期8-11,共4页
Journal of Zhejiang Normal University(Natoral Sciences)
关键词
二次系统
三次曲线解
极限环
唯一性
quadratic system
invariant cubic curve
limit cycle
uniqueness
