一类三次系统E_3~1的极限环与分支(英文)  

Limit Cycle and Bifurcation of a Kind of E_3~1 System

作　　者：周久红[1] 肖箭[1] 王瑀[1] 宋国强[2] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230601 [2]安徽医科大学卫生管理学院,安徽合肥230032

出　　处：《应用数学》2013年第3期686-692,共7页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation Project in Anhui Province of Department of Education(KJ2012A171);the Provincial Excellent Young Talents Fund Projects in Colleges in Anhui Province(2011SQRL126);the Anhui University of"211Project"Academic Innovation Team Pro-ject(KJTD002B)

摘　　要：本文利用微分方程几何理论,通过计算Hopf分支值,研究E13系统稳定性和极限环的存在性与不存在性.然后利用广义Liénard系统唯一性定理得到了系统极限化唯一性的若干充分条件.本文扩大了系统参数的范围,为平面E13系统提供了一个更为广泛的应用领域.According to the geometrical theory of differential equation by computiong the Hopf bifuraction values,the stability for a kind of Et system are developed to the existence and nonexistence of limit cycles. By using the uniqueness theorem of generalized Lienard system,some sufficient conditions on the uniqueness of limit cycles of the one is obtained. This works extend domain of parameter. Therefore a more extensive application domain for E1 polynomial systems is provided.

关 键 词：E3^1系统 极限环 唯一性 HOPF分支 

分 类 号：O175.1[理学—数学]