关于非线性Schrodinger微分系统的全局结构分析

Global Structure Analysis of a Class of Nonlinear Differential System

采用平移变换、Poincare变换、辅助微分方程等方法并结合matlab对一类非线性微分系统进行定性理论分析,得出该系统的有限平衡点和无穷远平衡点的拓扑性质以及附近轨线的走向,并从此证明了该系统在全平面上不存在极限环,进而获得该系统所有的全局结构图.

By using translation transformation,Poincare transformation,auxiliary differential equation and other methods and combining with matlab,this paper carries on a class of nonlinear differential system of qualitative theoretical analysis,and obtains the topological properties of limited equilibrium points and infinity equilibrium points of this system and the trend of nearby trajectory.Furthermore,it is proved that the system has no limit cycle in the whole plane,and then obtain all the global structure diagrams of this system.