Balancing with Noise and Delay

TL;DR

This paper investigates how delay and noise influence the stability of a random walk model, revealing an optimal delay that maximizes the time before escape from an unstable point, supporting the beneficial role of noise in balance control.

Contribution

It introduces a delayed random walk model with an unstable fixed point, demonstrating the existence of an optimal delay for balance stability, which is a novel insight.

Findings

Optimal delay maximizes first passage time.

Noise can enhance balance stability.

Delay influences the rate of escape from instability.

Abstract

Motivated by recent studies in human balance control, we study a delayed random walk with an unstable fixed point. It is observed that the random walker moves away from the unstable fixed point more slowly than is observed in the absence of delay. It is shown that, for given a noise level, there exists an optimal delay to achieve the longest first passage time. Our observations support recent demonstrations that noise has a beneficial role for balance control and emphasize that predicitive strategies are not necessary to transiently control balance.