某些分段李纳系统的Hopf分支环性数  

Cyclicity of Hopf bifurcation in some piecewise Liénard systems

作　　者：徐伟骄 XU Wei-jiao(School of Science,Tianjin University of Commerce,Tianjin 300134,China)

机构地区：[1]天津商业大学理学院,天津300134

出　　处：《沈阳航空航天大学学报》2021年第5期93-96,共4页Journal of Shenyang Aerospace University

基　　金：国家自然科学基金(项目编号:11801414)。

摘　　要：希尔伯特第16问题是著名数学家希尔伯特提出的涉及平面多项式系统极限环存在和分布问题的重要数学难题,此问题至今仍未彻底解决。基于此研究了某些平面分段李纳系统在原点附近的极限环分支问题。通过扰动,得到在原点附近由Hopf分支产生的环性数为N(m,n,1,2)=m-1,m,n∈{1,2,3}。Hilbert’s 16th problem is an important mathematical problem proposed by the famous mathematician Hilbert concerning the existence and distribution of limit cycles of plane polynomial systems.This problem has not been completely solved yet.Based on this,this paper studies the bifurcation of limit cycles near the origin of some piecewise Liénard systems.Through perturbation,the cyclicity generated by the Hopf bifurcation near the origin is N(m,n,1,2)=m-1,m,n∈{1,2,3}.

关 键 词：HOPF分支 分段光滑 李纳系统 环性数 希尔伯特第16问题 

分 类 号：O192[理学—数学]