Stochastic resonance in time-delayed bistable active particles

Abstract

We investigate analytically and numerically stochastic resonance in an underdamped active (Ornstein--Uhlenbeck) particle confined in a bistable potential with time-delayed feedback and subjected to an additional (non-thermal) white-noise source. Restricting the analysis to the active-noise-dominated bistable regime, with sufficiently short delay and active-noise correlation times, we develop a perturbative theory that yields analytical expressions for both the escape rate and the spectral power amplification within the framework of linear-response theory, without invoking detailed balance. The analytical predictions are in qualitative agreement with direct numerical simulations throughout the perturbative regime. We show that a moderate increase in the active-noise correlation time can enhance the stochastic-resonance response, in marked contrast to previous results for overdamped passive systems driven by colored noise. Conversely, the addition of white noise weakens the resonant response and shifts its optimum toward lower active-noise intensities. Time-delayed feedback further alters the matching condition between the escape rate and the driving frequency while preserving the resonant mechanism. Beyond the perturbative regime, we find that finite-memory effects progressively broaden the resonance profile and substantially decrease its amplitude. Overall, these results provide new insight into the combined role of inertia, activity, environmental fluctuations, and time delayed feedback in stochastic resonance in nonequilibrium systems.