基于指数型广义反射矩阵的微分系统与周期解  

The differential system and periodic solution based on the exponential generalized reflection matrix

作　　者：孙长军[1,2] 周正新[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]连云港职业技术学院,江苏连云港222006

出　　处：《扬州大学学报（自然科学版）》2011年第2期15-18,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60774073);江苏省高校自然科学基金资助项目(08KJB110013)

摘　　要：为了解决具有指数型广义反射矩阵的线性微分系统的周期解与稳定性问题,提出通过线性微分系统的广义反射矩阵来寻找其Poincaré映射的方法,研究了具有指数型广义反射矩阵的线性微分系统.x=P(t)x的条件,给出此类线性微分系统的广义反射矩阵的形式和广义反射函数,从而得到该类微分系统的周期解和稳定性.该结果对研究其他微分系统的周期解与稳定性具有一定的参考价值和指导意义.In order to solve the periodic solution and stability problem of linear differential system which has the exponential type generalized reflection matrix,this paper proposes a method seek for its Poincaré mapping by the generalized reflection matrix of the linear differential system.The author studies the condition of linear differential system =P（t）x that has the exponential type generalized reflection matrix,obtains the generalized reflection matrix form and the generalized reflection function of this kind of linear differential system,thus obtains their periodic solution and stability.This result has certain reference value and the guiding sense to study the periodic solution and the stability of other differential system.

关 键 词：广义反射函数 广义反射矩阵 线性微分系统 周期解 稳定性 

分 类 号：O175.13[理学—数学]