色噪声激励的时滞非线性系统瞬态响应研究  

Study on transient probability densities of delayed nonlinear system excited by colored noises

作　　者：戚鲁媛[1] 徐伟[1] 高维廷[2] 

机构地区：[1]西北工业大学理学院应用数学系,西安710129 [2]西北工业大学,电子信息学院,西安710129

出　　处：《计算机工程与应用》2013年第7期1-5,80,共6页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11172233,No.10932009,No.61171155);陕西省自然科学基金(No.2012JM8010);西北工业大学博士论文创新基金(No.CX201215)

摘　　要：建立了色噪声与时滞联合作用的非线性系统模型,提出求解其瞬态概率密度的高效近似算法。利用等价变换将时滞系统简化为非时滞系统;通过线性化方法和随机平均原理得到原系统振幅过程的平均It随机微分方程和相应的Fokker-Planck-Kolmogorov(FPK)方程。基于退化线性系统导出一组正交基,在该基空间内进行Galerkin变分得到近似瞬态概率密度。将该方法应用到受色噪声激励的双时滞Duffing-VanDerPol振子得到理论解,采用蒙特卡罗模拟(MCS)验证理论解的正确性。分析了色噪声参数和时滞参数对瞬态响应的影响。研究结果表明:所提理论方法可有效求解受色噪声激励的时滞非线性系统的瞬态概率密度;算法求解效率高于MCS;色噪声和时滞均明显影响了系统瞬态响应。An effective approach to calculate the transient probability densities of the multi-delayed nonlinear system driven by colored noise excitations is developed. The system with time delay is simplified to an equivalent system without time delay. The linearization technique and the stochastic averaging method are adopted to obtain the averaged It6 stochastic differential equation and the corresponding FPK （Fokker-Planck-Kolmogorov） equation for the amplitude process. A set of orthogonal base functions is obtained from the degenerated linear system. The Galerkin method is applied in the orthogonal base space to obtain the approx- imate probability densities. The proposed procedure is applied to the Duffing-Van Der Pol oscillator with two time delays and an external colored noise. The reliability of the theoretical results is verified by MCS （Monte Carlo simulation）. Effects of the colored noise and the time delay are also discussed. The results show that the proposed method is effective at studying the transient prob- ability densities of the time-delayed nonlinear system driven by colored noises; the theoretical calculation efficiency is higher than that of MCS; both of the colored noises and time delay affect the transient responses.

关 键 词：时滞 色噪声 FPK方程 瞬态概率密度 GALERKIN算法 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]