脉冲微分系统的数值模拟与可视化

Digital Simulation and Visualization of Impulsive Differential Systems

脉冲微分系统理论及应用研究近年来得到了很大的发展。对于一些较复杂的系统,进行理论分析很困难时,就必须利用数值模拟方法对其进行研究。研究对于脉冲微分系统进行数值模拟的算法设计问题。建立了动态赋值函数算法,并针对脉冲系统的特点,将求解微分方程数值解的龙格库塔法与脉冲点判别及处理有机结合,设计出求解脉冲微分系统的数值算法。由于可以方便地调用动态赋值函数算法,所设计的数值算法具有通用性。对一般的脉冲微分系统可求其数值解、绘制系统终态图及时间序列图等。选择了两类典型的脉冲微分系统为例,对其进行数值模拟,得到了一些有意义的结果。

The theory and application of impulsive differential systems have been greatly developed in recent years. For some complicated impulsive differential systems, it is very difficult to theoretically study them, and in this case, using numerical simulation technology to study them will be necessary. Numerical simulation algorithms is mainly studied for impulsive differential systems. An algorithm of assignment functions was established, and accord- ing to the characteristics of impulsive differential systems and using Runge-Kutta algorithm for ordinary differential equations as building blocks, combining with the method to determine the pulse. A new numerical algorithm is de- signed to address the differential systems with impulses. The new numerical algorithms can be applied to general impulsive differential systems to compute their numerical solution, to plot final state diagram and time series dia- gram. Two typical examples are discussed and the numerical simulations are carried out, some meaningful results are obtained.