# Delay sober up drunkers: Control of diffusion in random walkers

## TL;DR

This paper investigates how time-delayed feedback can suppress diffusion in stochastic random walks, revealing that increasing delay reduces diffusion, supported by analytical and molecular dynamics simulations.

## Contribution

It introduces a novel approach to controlling diffusion in stochastic processes using time-delayed feedback, combining analytical and simulation methods.

## Key findings

- Diffusion coefficient decreases as delay time increases.
- Time delay feedback effectively suppresses diffusion in random walks.
- Analytical results align with molecular dynamics simulations.

## Abstract

Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic process, i.e., a random walk and observe its diffusion phenomenon with time delayed feedback. Surprisingly, the diffusion coefficient decreases with increasing the delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying the time-delay feedback to a molecular dynamics model.