Delayed Random Walks and Control

TL;DR

This paper explores resonance phenomena in non-standard delayed random walk models, demonstrating how tuning bias and delay can enhance stability and modeling complex systems like string entanglement.

Contribution

It introduces and analyzes two novel delayed random walk models, revealing resonant effects that improve stability and model entanglement phenomena.

Findings

Resonant effects improve stability in repulsive delayed random walks.

Tuning bias and delay enhances fixed point stability.

Resonant phenomena observed in sticky random walks.

Abstract

Issues of resonance that appear in non-standard random walk models are discussed. The first walk is called repulsive delayed random walk, which is described in the context of a stick balancing experiment. It will be shown that a type of "resonant" effect takes place to keep the stability of the fixed point better with tuned bias and delay. We also briefly discuss the second model called sticky random walk, which is introduced to model string entanglement. Peculiar resonant effects with respect to these random walks are presented.