摘要
运用ＧＳａｎｓｏｎｅ定理和旋转向量场理论，研究奇次微分系统ｘ＝－ｙ（１－ａｘ）（１－ｂｘ）＋δｘ－ｌｘ２ｎ＋１，ｙ＝ｘ（１－ａｘ）（１－ｂｘ）的极限环的存在唯一性．证明了：当δｌ≤０时不存在极限环；当δｌ＞０，｜δ｜＜｜ｌ｜ｍａｘ｛ａ２ｎ，ｂ２ｎ｝时存在唯一的极限环；当δｌ＞０，｜δ｜≥｜ｌ｜ｍａｘ｛ａ２ｎ，ｂ２ｎ｝时不存在极限环；当δｌ＞０，ａ＝ｂ＝０时存在唯一的极限环，若极限环存在，则当δ＞０时是稳定的。
Based on the G. Sansome theorem and the theory of rotated vector fields,the existence and uniqueness of limit cycles of differential systems=-y(1-ax)(1-bx)+δx-lx2n+1,=x(1-ax)(1-bx)are studied. The conclusions are:if δl≤0 or δl>0 and|δ|≥|l|max{a2n,y2n} the limit cycles are not exist;if δl>0 and |δ|<|l|max{a2n,b2n}or δl> and a=b=0, the limit cycles are exist.If the limit cycles exist and δ>0 the limit cycles are instable; if the limit cycles exist and δ<0,the limit cycles are instable.
出处
《宁夏大学学报（自然科学版）》
CAS
1997年第4期316-319,共4页
Journal of Ningxia University(Natural Science Edition)
关键词
微分系统
极限环
存在性
唯一性
Differential systems
limit cycles
existence
uniqueness
