Stochastic resonance induced by a multiplicative periodic signal in a bistable system with cross-correlated noises and time delay

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a bistable system with cross-correlated noises and time delay is studied. Two cases have been considered: the case of a system with no delay and the case of a system with time-delayed feedback. The expressions for the signal-to-noise ratio (SNR) are derived, for both cases. The effects of the cross-correlated noise intensity (lambda) and the delay time (tau) on the SNR are discussed. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomenon. In contrast with the case for the SR induced by an additive signal, here both lambda and tau have critical values in SR when the SNR as a function of the noise intensities, i.e., lambda (or tau), suppresses the SR for lambda (or tau) below the critical value while it enhances the SR for lambda (or tau) above the critical value. tau suppresses the SR in the SNR as a function of. while it enhances the SR in the SNR as a function of the noise intensities. The SNR is not only dependent on lambda, tau and the noise intensities, but also on the initial condition of the system.