基于对角广义反射矩阵的线性微分系统及其周期解

Linear differential system and periodic solution based on diagonal generalized reflection matrix

为了解决具有对角广义反射矩阵的线性微分系统周期解与稳定性问题,采用通过广义反射函数寻找其Poincaré映射的方法.首先在广义反射函数定义下,给出可交换线性微分系统的反射矩阵的定义及广义反射矩阵的一般形式,得到具有对角广义反射矩阵的线性微分系统的广义反射矩阵,然后通过对角广义反射矩阵找到Poincaré映射,从而得到该类系统的周期解及稳定性,并推得二维线性微分系统的周期解与稳定性.由于广义反射函数解决周期解稳定性比其他方法具有很大的优势,所以,此种方法对研究相关微分系统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 periodic solution and the stability problem with the opposite angle generalized reflection matrix linear differential system,it used the method of seeking for its Poincaré map using the generalized reflection function.Firstly,in a generalized reflection function sense,It gave the reflection matrix definition and the generalized reflection matrix general form of the exchangeable linear differential system,obtained the generalized reflection matrix of the linear differential system with the diagonal generalized reffection matrix,finally found the Poincaré map through the opposite angle generalized reflection matrix,thus obtained its periodic solution and stability,and got periodic solution and stability of the two-dimensional linear differential system.Because the generalized reflection function solution periodic solution stability was superior comparing to other methods,this method had certain reference value and the guiding sense to study the relate differential system periodic solution and the stability.