| Abstract: |
| We study stochastic resonance in a bistable active model driven by periodic forcing, time-delayed feedback, and both white and colored noise. Using a probability-density approach, linear response theory, and numerical simulations, we analyze the appereance of stochastic resonance. In the small-delay regime, we derive analytical expressions for the stationary probability density, escape rates, and spectral amplification by combining a perturbative treatment of the delayed dynamics with a WKB-like approximation. Our results show that white and colored noise play competing roles: white noise tends to wash out memory effects, whereas colored noise introduces persistence that can reshape barrier crossing and resonance. Time delay also strongly modulates the dynamics by altering the effective stability of the bistable states and the noise-activated transition rates. Numerical simulations of the stochastic delay equations confirm the analytical predictions and reveal a non-monotonic dependence of the resonance on noise strength, delay, and noise correlation time. These results clarify how memory and non-equilibrium fluctuations jointly control bistable stochastic dynamics. |
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