一类奇次系统极限环的存在唯一性研究

A Study of the Existence and Uniqueness of Limit Cycle for a Type of Odd Order Systems

利用Sansone定理和旋转向量场理论对平面奇次系统.x=-y(1-ax)(1-bx)+δx-lx2n+1、.y=x(1-ax)(1-bx)进行了全面的分析,得到其极限环的存在性、唯一性及不存在性的完整结果。

By means of Sansone＇s Theorem and Theory of rotation vector fields, differential systems X = -y^·（ 1 -ax ） （ 1 - bx ） ＋δx - Lx2n＋1, y^·= x（ 1 - ax ） （ 1 - bx ）are analyzed comprehensively, The existence, uniqueness and nonexistence are investigated, and the complete results are obtained.