东南大学学报（英文版）
東南大學學報（英文版）
동남대학학보（영문판）
JOURNAL OF SOUTHEAST UNIVERSITY
2004年
4期
517-520
,共4页
二次微分系统%极限环%细焦点
二次微分繫統%極限環%細焦點
이차미분계통%겁한배%세초점
quadratic differential system%limit cycle%weak focus
研究了特殊Ⅲ类二次微分系统(x)＝-y+lx2+mxy,(y)＝x(1+ax+by)的极限环的最大个数问题. 纠正了索明霞和岳锡亭的文章(微分方程年刊, 2003,19(3):397401)中的一些错误. 通过将所研究的系统化为Liénard型系统并利用其相关性质给出了几个定理, 在某些条件下证明了系统最多存在2个极限环, 改进了上述一文中的结果.
研究瞭特殊Ⅲ類二次微分繫統(x)＝-y+lx2+mxy,(y)＝x(1+ax+by)的極限環的最大箇數問題. 糾正瞭索明霞和嶽錫亭的文章(微分方程年刊, 2003,19(3):397401)中的一些錯誤. 通過將所研究的繫統化為Liénard型繫統併利用其相關性質給齣瞭幾箇定理, 在某些條件下證明瞭繫統最多存在2箇極限環, 改進瞭上述一文中的結果.
연구료특수Ⅲ류이차미분계통(x)＝-y+lx2+mxy,(y)＝x(1+ax+by)적겁한배적최대개수문제. 규정료색명하화악석정적문장(미분방정년간, 2003,19(3):397401)중적일사착오. 통과장소연구적계통화위Liénard형계통병이용기상관성질급출료궤개정리, 재모사조건하증명료계통최다존재2개겁한배, 개진료상술일문중적결과.
The maximal number of limit cycles for a particular type Ⅲ system (x)＝-y+lx2+mxy,(y)＝x(1+ax+by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003, 19(3):397401) are corrected. By translating the system to be considered into the Liénard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above.
