摘要
利用反射函数理论来讨论四阶线性微分系统的下三角反射函数的存在性,并计算出在不同情况下具体的反射矩阵.同时,利用反射矩阵来建立周期微分系统的庞加莱映射,进而该系统周期解的存在稳定性判定定理也相应地建立起来.最后,将以上结果推广应用到了非线性微分系统中.
In this paper, we use the reflective function theory developed by Mironenko to discuss the existence of the lower triangular reflective matrix of the fourdimensional linear differential system, and then compute the specific reflective matrix under some given conditions. Meanwhile, we make use of this reflective matrix to establish the poincaré map of the 2ω-periodic system, and the decision theorem of the existence and stability of this system's periodic solution is established as well.In addition,we spread and apply these results of linear differential system to the non-linear differential system.
作者
郭嘉宾
陈玉福
GUO Jiabin;CHEN Yufu(University of Chinese Academy of Sciences, Beijing 100049)
出处
《系统科学与数学》
CSCD
北大核心
2017年第10期2052-2069,共18页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11271363)资助课题
关键词
线性微分系统
下三角反射矩阵
周期解
Linear differential system, lower triangular reflective matrix, periodic solution.