Controlling noise with self-organized resetting.

Biological systems often consist of a small number of constituents and are therefore inherently noisy. To function effectively, these systems must employ mechanisms to constrain the accumulation of noise. Such mechanisms have been extensively studied and comprise the constraint by external forces, nonlinear interactions, or the resetting of the system to a predefined state. Here, we propose a fourth paradigm for noise constraint: self-organized resetting, where the resetting rate and position emerge from self-organization through time-discrete interactions. We study general properties of self-organized resetting systems using the paradigmatic example of cooperative resetting, where random pairs of Brownian particles are reset to their respective average. We demonstrate that such systems undergo a delocalization phase transition, separating regimes of constrained and unconstrained noise accumulation. Additionally, we show that systems with self-organized resetting can adapt to external forces and optimize search behavior for reaching target values. Self-organized resetting has various applications in nature and technology, which we demonstrate in the context of sexual interactions in fungi and spatial dispersion in shared mobility services. This work opens routes into the application of self-organized resetting across various systems in biology and technology.