一类二次系统的极限环分布和Hopf分支  

Hopf bifurcation and limit cycles for a class of quadratic differential system

作　　者：原冠秀[1,2] 窦霁虹[1] 赵书红[1] 

机构地区：[1]西北大学数学系,陕西西安710127 [2]河南科技学院数学系,河南新乡453003

出　　处：《西北大学学报（自然科学版）》2010年第3期385-388,共4页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省自然科学基金资助项目(2003A07)

摘　　要：目的研究一类二次微分系统的极限环存在性及唯一性。方法运用Dulac判别法对极限环的分布进行讨论,并利用Hopf分支理论讨论了极限环的存在性、唯一性及稳定性。结果得到了此类系统极限环存在且唯一的充分条件。结论此类系统极限环具有存在性、唯一性和稳定性。Aim To discusses the existence and uniqueness of limit cycles for a class of quadratic system. Methods Dulac discriminance is applied to discuss the nonexistence of limit cycles for a class of quadratic system,and based on the Hopf bifurcation theory,the existence,uniqueness and stability on limit cycles are studied. Results The sufficient conditions of the existence,uniqueness on limit cycles are derived. Conclusion The existence,unique-ness and stability on limit cycles for this system are obtained. The results of this system are renewed.

关 键 词：二次微分系统 极限环 DULAC函数 HOPF分支 

分 类 号：O175.12[理学—数学]