Stochastic Resonance in Time-delayed Bistable Systems Driven by Weak Periodic Signal

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We study theoretically a bistable systems with time-delayed feedback driven by weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of signal. The maximum of SNR decreases with increasing the feedback intensity ε. When ε is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.