Noise

Noise-Induced Resonance in Periodically Driven Run-and-Tumble Bacterial Suspensions

Abstract

Noise is generally regarded as a source of disorder in active matter, yet its role in periodically driven bacterial suspensions remains poorly understood. Here, we use particle-based simulations to investigate whether stochastic tumbling can enhance the collective response of a quasi-two-dimensional suspension of run-and-tumble bacteria subjected to weak periodic motility modulation. The unforced system exhibits a transition from a homogeneous active fluid to a clustered state below a critical tumbling rate of approximately 0.42 s⁻¹, establishing the intrinsic relaxation timescale of the suspension. Under subthreshold forcing, the structural response displays a clear resonance at an intermediate tumbling rate, where the active-pressure oscillation increases by approximately 5.4-fold and the mechanical hysteresis area by 4.6-fold relative to the low-noise state. Increasing temperature shifts the optimal tumbling rate from 0.26 to 1.30 s⁻¹, reduces the maximum structural response by about 94%, and shortens the relaxation time by more than one order of magnitude. Nevertheless, both structural and mechanical responses collapse onto universal master curves when expressed as a function of  demonstrating that collective synchronization is governed by relaxation-time matching between stochastic tumbling and periodic forcing. These findings provide a simple framework for controlling organization and mechanical response in active bacterial suspensions.