Anti-persistent random walks in time-delayed systems

TL;DR

This paper demonstrates that chaotic diffusion in certain time-delayed systems can be modeled as an anti-persistent random walk, with detailed analysis of how nonlinearity and delay influence the process.

Contribution

It introduces a novel description of chaotic diffusion in time-delayed systems using anti-persistent random walks and analyzes the impact of system parameters on this behavior.

Findings

Chaotic diffusion can be modeled as an anti-persistent random walk.

The diffusion coefficient depends on nonlinearity and delay parameters.

Markov processes of increasing order describe the system as nonlinearity decreases.

Abstract

We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the dependence of all relevant quantities characterizing the random walk on the strength of the nonlinearity and on the delay. With the help of analytical considerations, we show that for a decreasing nonlinearity parameter the resulting dependence of the diffusion coefficient is well described by Markov processes of increasing order.