常微平面自治系统相图的计算机辅助研究

Computer Assisted Study of Phase Graph of Autonomous System on Plane of Ordinarily Differential Equation

研究利用微机绘制常微分方程平面自治系统相图的方法 ,首先用一种合适的数值算法由已知的初始条件得到轨线的大量数据 ,再利用这些数据在计算机屏幕上画出轨线的图形。设计了一个实用程序 ,通过试验与理论分析相结合 ,获得了 3个著名自治系统的精确相图 ,直观表明了这些系统的变化规律 ,它们是对理论分析方法的补充。

The method using microcomputer to draw the phase graph of autonomous system on plane of ordinarily differential equation is studied,first a large number of data of orbit are obtained by an appropriate method of numerical calculation from known initial condition,then computer draw the curve of orbit on screen by these data. A applied program is designed, accurate phase graphs of three famous atonomous systems are obtained by test and theoretic analysis, these graphs intuitively illustrate variational trend of the systems,they are complement for method of abstract theory.