PERIODICALLY DRIVEN LINEAR-SYSTEM WITH MULTIPLICATIVE COLORED NOISE

A periodically driven Linear system subject to multiplicative correlat ed noise is considered. It has been argued recently by several authors that such a simple system exhibits stochastic resonance. By introduci ng a general type of composite stochastic process, bridging two previo usly considered limiting cases of dichotomous and Gaussian noise, it i s proved that, indeed, the amplitude of the average of the driven line ar process at long times shows a pronounced maximum both as a function of the noise strength and as a function of the autocorrelation time. However, this kind of stochastic resonant behavior can be experimental ly observable only in a special case where the initial phase of the ex ternal forcing is somehow fixed. Additional averaging over the uniform distribution of the initial random phase, inherent in most physical s ystems, leads to that the periodic output vanishes identically at long times. Moreover, the system response is typically defined in terms of the power spectrum rather than the amplitude of the average. The outp ut signal given by the spectral density corresponding to the frequency of the external forcing is calculated via the long-time phase-average d correlation function. It appears that the output signal simply diver ges upon approaching the second moment instability point with increasi ng noise strength. No stochastic resonance is observed for any paramet er settings. Interestingly, the resonancelike behavior of the system r esponse as a function of the autocorrelation time is retained.