中文摘要：

本文研究了周期调制噪声驱动的具有质量涨落的欠阻尼谐振子的随机共振，其中的振子质量的涨落为对称双态噪声而内噪声为高斯噪声．通过Shapiro—Loginov公式和Laplace变换，本文得到了系统稳态响应的一阶矩的解析表达式，接着利用Routh—Hurwitz判据推导了系统响应的一阶矩的稳定性条件，进而通过数值仿真研究了系统响应的一阶矩与系统各参数间的依赖关系．仿真结果表明稳态响应振幅与周期输入信号频率、涨落噪声参数及系统固有参数均呈非单调变化关系，模型出现真实共振、广义随机共振和参数诱导共振等丰富的随机共振现象．进而，本文的研究还表明质量涨落噪声和周期信号调制噪声的相互协作将导致系统的一些新的共振效应出现，比如关于系统稳态响应振幅与驱动频率的双峰共振及关于某些噪声参数的单谷共振行为．

英文摘要：

In this paper, stochastic resonance of an underdamped harmonic oscillator with random mass and driven by periodic modulated noise is investigated. The fluctuation of oscillator mass is modeled by a dichotomous noise while the internal noise is assumed to be Gaussian. Using the Shapiro-Loginov formu- la and the Laplace transform technique, exact expressions of first moment of the steady-state response and output of the system are presented. Then some simulations are implemented to study the dependence of long-time behavior of the first moment on variety of the system parameters. It is shown that the out- put amplitude non-monotonically depends on the signal frequency, the noise parameters and the system parameters, which indicates the occurrences of bona fide stochastic resonance, generalized stochastic resonance and parameter-induced stochastic resonance. Furthermore, based on the exact expressions it is demonstrated that interplay of the mass fluctuation and the periodic modulated noise can generate some novel cooperation effects, such as double-peak resonance as well as one-valley resonance.