含时滞反馈与涨落质量的记忆阻尼系统的随机共振

针对具有记忆效应的欠阻尼系统, 存在时滞反馈与涨落质量, 本文主要研究了其输出稳态响应振幅的随机共振效应. 首先通过引入新变量和运用小时滞近似展开理论, 将具有非马尔科夫特性的原系统转化为等价的两维马尔科夫线性系统, 再利用Shapiro-Loginov公式和Laplace变换获得了系统响应的一阶稳态矩和稳态响应振幅的解析表达式. 结果表明: 当系统参数满足Routh-Hurwitz稳定条件时, 稳态响应振幅随质量涨落噪声强度、周期驱动信号频率以及时滞的变化均存在随机共振现象, 其中随机多共振现象也被观察到. 在适当范围内, 通过控制时滞反馈, 系统的随机共振效应随着时滞的增大而增强, 而较长的记忆时间及增大阻尼参数均对共振行为呈现抑制作用.有效调控时滞反馈与记忆效应的变化关系将有助于增强系统对周期驱动信号的响应强度. 最后, 通过数值模拟计算验证了理论结果的有效性. 

STOCHASTIC RESONANCE OF A MEMORIAL-DAMPED SYSTEM WITH TIME DELAY FEEDBACK AND FLUCTUATING MASS

The stochastic resonance (SR) in the memorial under-damped system with time delay feedback and fluctuating mass is investigated in this paper. The non-Markovian original system is reformulated into two-dimensional Markovian linear system through introducing variable transformations and using the small time delay approximation. Further, the analytic expressions for the first moment of the response and the steady response amplitude are derived by using the Shapiro-Loginov formula and the Laplace transformation technique. All the research results show that when the Routh-Hurwitz stability is satisfied, the phenomenon of SR is shown with the variations of mass fluctuation noise intensity, driving frequency and time delay, respectively. The stochastic multi-resonance phenomenon is also observed. Moreover, the SR is enhanced with an increase in time delay by introducing the time delay feedback and instead, the SR is suppressed for large memory time and damping parameter. By adjusting the time delay feedback and the memory effects, the response of the system to a harmonic signal can be further improved. Finally, the theoretical results are well verified through numerical simulations