非线性系统Hopf分叉临界点的稳定性  

Stability analysis of nonlinear system at critical point of Hopf bifurcation

作　　者：陈宇东[1] 裴春艳[1] 曹宗杰[2] 

机构地区：[1]吉林大学机械科学与工程学院,长春130022 [2]空军航空大学机械工程系,长春130022

出　　处：《吉林大学学报（工学版）》2009年第4期993-996,共4页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家自然科学基金项目(10202006);吉林大学'985工程'项目

摘　　要：由于参数的小扰动,非线性系统Hopf分叉临界点的亏损特征值可分离为密集特征值。利用Puiseux展开式讨论了Hopf分叉临界点的特征值分叉现象,同时讨论了在临界点的响应显式解。这些结果具有明确的物理意义,并可用来说明非线性系统在Hopf分叉临界点附近的不稳定性的机理。最后给出了本文方法在机翼模型中的应用。Due to a small change of the parameter, non-semi-simple eigenvalues of the linearized approximation of the nonlinear system may separate into close eigenvalues. By using the Puiseux expansion, the eigenvalue bifurcation at critical point of Hopf bifurcation was developed. An explicit expression of the response at the near critical point was also developed. These results can provide good physical insight and can be used to explain the mechanism of the stability of the nonlinear system at the near critical point. An example, the flutter problem of an airfoil in simplified model, was given to illustrate the application of the proposed method.

关 键 词：固体力学 非线性系统 Hopf分叉的临界点 特征值分叉 稳定性分析 

分 类 号：O326[理学—一般力学与力学基础]