非线性临界系统稳定性分析的中心流形方法  

Center manifold method for stability analysis of nonlinear systems in critical cases

作　　者：刘向东[1] 黄文虎[1] 

机构地区：[1]哈尔滨工业大学航天工程与力学系,黑龙江哈尔滨150001

出　　处：《哈尔滨工业大学学报》1999年第6期1-4,共4页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金!(19990510)

摘　　要：为了揭示临界模态或近临界模态与工程力学系统的振荡、分叉、失稳的内在联系，结合中心流形定理，建立了非线性临界系统稳定性分析的一般方法． 在Ｈｏｐｆ 分叉理论研究基础上，研究了具有周期性临界模态（ 线性化系统含有一对纯虚特征值） 的非线性系统稳定性，获得了临界渐进稳定、不稳定的充分条件，给出的相应稳定性判据计算简单，形式直观简捷． 结果表明临界情形下的非线性系统稳定性不仅与非线性项有关，而且与其线性化系统的特征值存在密切联系．A general method is proposed for stability analysis of nonlinear systems in critical cases for the purpose of revealing the inherent relationship between the critical mode (near critical mode) between the oscillation、bifurcation or loss of stability of engineering mechanical systems. By center manifold theorem and Hopf bifurcation theory, the stability of nonlinear systems with periodically critical mode(i.e.,the linearized systems have a pair of pure imaginary eigenvalues) has been studied and the sufficient conditions of stability of the critical systems are obtained,the stability criterion was intuitionistic、simple and easy to calculate. The results show that the stability of nonlinear systems in critical cases is not only related to the nonlinearity terms, but also to the eigenvalues of the linearized system.

关 键 词：非线性系统 HOPF分叉 中心流形 稳定性 临界模态 

分 类 号：TP271.62[自动化与计算机技术—检测技术与自动化装置] TP13[自动化与计算机技术—控制科学与工程]