一类高维非线性微分系统及其截断系统的等价性  

Equivalence Between a Class of High Dimensional Nonlinear Differential Systems and Their Truncated Systems

作　　者：周坚[1] ZHOU Jian(College of Liberal Arts and Science,Suqian University,Suqian 223800,China)

机构地区：[1]宿迁学院文理学院,江苏宿迁223800

出　　处：《数学的实践与认识》2021年第22期284-293,共10页Mathematics in Practice and Theory

基　　金：宿迁市科技计划项目(2019096);国家自然科学基金面上项目(11971475)。

摘　　要：综合运用反射函数与反射积分,首先研究三维非自治微分系统与其截断系统等价的充要条件,并探讨该三维非线性微分系统的结构形式,然后进一步探讨该微分系统解的周期性.所得结论推广了相应二维微分系统的相关成果.In this paper,we firstly study the necessary and sufficient conditions for the equivalence of three-dimensional nonautonomous differential systems and the corresponding truncated system and the structure of such nonlinear systems.And then we apply the obtained results to the study of the periodicity of their solutions when such systems are periodic systems int.The obtained conclusions extend the related results of the corresponding two-dimensional differential system.

关 键 词：反射函数 反射积分 等价性 周期解 

分 类 号：O175[理学—数学]