一类三次系统的奇闭轨与极限环  

SINGULAR CLOSED TRAJECTORY AND LIMIT CYCLE OF A CLASS THREETIMES SYSTEM

作　　者：侯劲 代立新 

机构地区：[1]宜昌师范高等专科学校 [2]荆州师范高等专科学校

出　　处：《数学杂志》1996年第3期381-384,共4页Journal of Mathematics

摘　　要：本文运用旋转向量场理论，推广了文［１］的一个结论；证明了系统ｄｘｄｔ＝－ｕｘ＋２ｙ＋ｖｘ３＋ｗｘｙ２－２ｙ３，ｄｙｄｔ＝ｘ＋ｘ３在一定条件下具有“８字形奇闭轨”，并且它的外面至少还有一环；适当选取ｕ，ｖ，ｗ的值。This paper apply theory of rotated vector field to extend a conclusion of the paper , It is proved that under certain condition, the system dxdt=-ux+2y+vx 3+wxy 2-2y 3, dydt=x+x 3 , have a singular closed trajectory of the form “8”, and exist at least a limit cycle outside the singular closed trajectory; Choosing proper values of u,v,w , the system have at least five limit cycles.

关 键 词：奇闭轨 旋转向量场 三次系统 极限环 常微分方程 

分 类 号：O175.1[理学—数学]