时滞反馈力作用下含有分数阶阻尼的随机系统的响应与分叉研究

摘要

In this paper, the response and bifurcation of fractional stochastic systems with time-delayed feedback control are investigated.We decompose the time-delayed items and apply the stochastic averaging method with the generalized harmonic functions to obtain the stationary response.The effectiveness of the method is verified by two different examples.The simulation results show that different system parameters can affect the response of the system, and it can induce the occurrence of stochastic bifurcation for some certain systems as well.%分析了时滞反馈力作用下含有分数阶阻尼的随机系统,并讨论了该系统的稳态响应及随机分叉.首先,通过对含有时滞项的近似处理以及基于广义谐和函数的随机平均法得到了该系统的稳态响应.然后使用算例对方法的有效性进行了验证,其中主要研究了时滞反馈作用力和分数阶阻尼对系统稳态响应的影响,结果表明上述两者的变化会影响系统的稳态响应并引发随机分叉现象.