Random walks with asymmetric time delays

TL;DR

This paper investigates how asymmetric time delays influence the behavior of simple random walks, revealing that delays affect the mean position and can be manipulated to reverse its direction.

Contribution

It introduces a novel analysis of asymmetric time delays in random walks, combining simulations and analytical approximations to uncover new dynamic behaviors.

Findings

Mean position depends on time delays

Time delays can be reversed by shifting fitness functions

Stochasticity and delays jointly influence walk dynamics

Abstract

We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has been observed. Namely, the mean position of a walker depends on time delays. This is a joint effect of both stochasticity and time delays present in the system. We also observed that by shifting appropriately fitness functions we may reverse the effect of time delays - the mean position of the walker changes the sign.