一类E_3~1系统极限环的定性分析

Qualitative Analysis of Limit Cycles of a E_3~1 System

为了研究一类E_3~1系统的极限环的存在性和唯一性问题,引入Liapunov级数和Poincaré变换,讨论奇点类型,运用3种常用方法分析了极限环的不存在性,同时应用Hopf分支理论及Poincaré-Bendixson环域定理给出极限环的存在性和唯一性的充分条件。

The paper investigates the existence and uniqueness of limit cycle of E_3~1 system. By introducing Liapunov series and transformation of Poincaré to discuss the type of its limited singular point and infinite point. Then the sufficient conditions for nonexistence of limit cycle are given by using three common methods. Meantime,by applying Hopf bifurcation theory and PoincareBendixson＇s ring domain theorem,we generalize the sufficient conditions for the existence and uniqueness of limit cycle.