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

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.