Stochastic resonance (SR) in a harmonic oscillator with parametric bounded noise and external periodic force is investigated. By applying the property of bounded noise and using Cameron–Martin formula, infinite chains of linear differential equations are obtained for the spectral amplification, mean-square displacement, and variance. Multiple stochastic resonances are observed for these characteristics. Relationships with resonant tongues of the Mathieu equation are established. It is shown that similar effects can be observed in the case of harmonic noise external force. The case of two coupled oscillators is also studied. Analysis is based on a natural truncation of the infinite moment chains and using of the numerical matrix computations.

研究了具有参数有界噪声和外部周期性力的谐波振荡器的随机共振（SR）。通过应用有界噪声的属性并使用Cameron-Martin公式，可以获得用于光谱放大，均方位移和方差的线性微分方程的无限链。对于这些特性，观察到了多种随机共振。建立了与Mathieu方程的共振舌的关系。结果表明，在谐波噪声外力的情况下可以观察到类似的效果。还研究了两个耦合振荡器的情况。分析基于无限矩链的自然截断和数值矩阵计算的使用。