Stochastic resonance in a periodically driven linear system with multiplicative and periodically modulated additive white noises

The stochastic resonance (SR) of periodically driven linear system with multiplicative white noise and periodically modulated additive white noise is studied. Exact expressions of output signal-to-noise ratio are obtained. The SR characteristics features are shown in two different situations: The driven frequency Ω is equal to the modulative frequency Ω1 and the driven frequency Ω is not equal to the modulative frequency Ω1. The result was as follows. The exact expression of output signal-to-noise ratio (SNR) exhibits SR in three aspects in the case of Ω=Ω1: (1) The curve of SNR versus noise strength Q exists a resonance peak. This is a standard form of SR. (2) A resonance peak exists in the SNR vs λ curve in the region of λ>0. (3) A maximum appears in the curve of SNR as a function of the characteristic of signal itself, the signal frequency Ω. It is of interest to examine the SNR in the case of Ω≠Ω1. From the exact expression of SNR we see, for Ω≠Ω1, that the SNR vs Q curve exhibits a minimum firstly, then a maximum, that is to say, it exhibits a suppression firstly, resonance later and is very different from the case of Ω=Ω1.