Frequency Selective Collective Dynamics in Periodically Driven Run-and-Tumble Bacterial Suspensions

Abstract

Collective dynamics in active bacterial suspensions are governed by interactions between self-propulsion, local crowding and environmental fluctuations, yet the influence of periodically modulated motility remains poorly understood. Here, we investigate a quasi-two-dimensional suspension of run-and-tumble bacteria whose swimming speed decreases with local density and is periodically modulated using particle-based simulations. The unforced system undergoes a transition from a homogeneous active fluid to a clustered state with finite structural correlations and a non-monotonic active pressure, with clustering emerging at a critical area fraction of . Periodic modulation produces three distinct dynamic regimes: quasistatic response at low frequencies, frequency-selective amplification at intermediate frequencies, and effective time averaging at high frequencies. The strongest collective response occurs near , where the driving period matches the intrinsic cluster-relaxation time. Increasing temperature shifts the optimal reduced frequency to higher values while suppressing the maximum clustering response, whereas intermediate density-dependent slowing  yields the largest dynamic susceptibility. Furthermore, response curves obtained under different temperatures and slowing strengths collapse onto universal master curves when scaled by the optimal reduced frequency, demonstrating that both parameters primarily rescale the intrinsic relaxation time. These findings establish a simple framework for frequency-controlled organization and mechanical regulation of active bacterial suspensions.