Effects of time delay on stochastic resonance of a periodically driven linear system with multiplicative and periodically modulated additive white noises

Stochastic resonance (SR) of a periodically driven time-delayedlinear system with multiplicative white noise and periodicallymodulated additive white noise is investigated. In the condition ofsmall delay time, an approximate analytical expression of outputsignal-to-noise ratio (SNR) is obtained. The analytical resultsindicate that (1) there exists a resonance peak in the curve forSNR versus time delay; (2) the time delay will suspend the SRdramatically for SNR versus other parameters of the system, such asnoise intensity, correlation intensity, and signal frequency, once acertain value is reached, the SR phenomenon disappears.