宽带噪声激励下含分数阶时滞系统的随机分岔  

Stochastic Bifurcation of Fractional-Order Delay Feedback System under Broadband Noise

作　　者：盛正大 王媛 王慧男 王芳 SHENG Zheng-da;WANG Yuan;WANG Hui-nan;WANG Fang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou Gansu 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《菏泽学院学报》2023年第5期6-13,共8页Journal of Heze University

摘　　要：研究了在外部宽带噪声激励下含分数阶耦合时滞反馈的Van der pol系统的随机分岔.利用一组拟周期函数近似替换分数阶微分,通过随机平均法得到系统的伊藤随机微分方程,进一步求出与系统幅值相关的平稳概率密度函数.使用Matlab绘制联合概率密度图,直观地展现了系统发生的稳态变化,并依据图像分析在时滞参数与分数阶阶次分别改变的情况下系统产生的随机P-分岔.结果表明时滞参数和分数阶阶次会对Van der pol系统的动力学特性产生影响,即当时滞参数和分数阶阶次在一定阈值内变化时,会诱导Van der pol系统产生P-分岔现象.This study explores the stochastic bifurcation of a Van der Pol system with fractional-order coupled time-delay feedback subjected to external broadband noise.A set of quasi-periodic functions was employed to replace the fractional-order differential elements.Subsequently,the stochastic averaging method was employed to establish a first-order stochastic differential equation for the system.The stationary probability density function associated with the system’s amplitude was determined.Utilizing Matlab,joint probability density plots were created to intuitively illustrate the steady-state changes in the system.Based on image analysis,the study examined the occurrence of stochastic P-bifurcation in the system under varying delay parameters and fractional-order conditions.The results indicate that changes in delay parameters and fractional-order have a significant impact on the dynamic characteristics of the Van der Pol system.Specifically,when both delay parameters and fractional-order are varied within certain threshold values,it induces the occurrence of P-bifurcation phenomena in the Van der Pol system.

关 键 词：随机P-分岔 随机平均法 Van der pol方程 平稳概率密度函数 宽带噪声 

分 类 号：O324[理学—一般力学与力学基础] O175[理学—力学]