摘要
引入噪声时的Duffing方程是一个二阶非线性随机微分方程,由于无法求得该随机微分方程的精确解析解,所以绝大多数情况下利用Simulink仿真模型,采用龙格库塔算法求Duffing方程的数值解。针对龙格库塔算法在每一步积分迭代过程中计算量大,导致系统进入稳态解的时间过长的问题,通过对布朗运动及其积分的分析,利用"欧拉-丸山"算法求解Duffing系统中的随机微分方程。经仿真计算,欧拉-丸山算法可以正确描述Duffing方程丰富的混沌动力学特性,而且在求解过程中能方便地定义随机积分方程中的噪声信号。仿真结果表明与常用的龙格库塔方法相比,"欧拉-丸山"算法具有较为明显的时间复杂度优势。
The moment equations of Duffing oscillator in the presence of noise and weak periodic signal are typical stochastic differential equations（SDE）.Because of the presence noise,it is impossible to get the exact solutions to these equations.Simulink model and Runge-Kutta algorithm are usually used to solute SDE.In this paper,how the Euler-Maruyama method can be used to numerically simulate the SDE of Duffing oscillator is studied.The numerical results show that Euler-Maruyama method can effectively simulate Duffing oscillator.Especially,the simulation elapsed time of this method is much shorter than that of the usually used methods.
出处
《电子测量技术》
2011年第3期37-40,61,共5页
Electronic Measurement Technology
