Noise Induced Pattern Switching in Randomly Distributed Delayed Swarm Patterns

TL;DR

This paper investigates how noise influences pattern switching in a swarm of self-propelling particles with randomly distributed time delays, revealing a critical noise level that induces more organized swarm states.

Contribution

It introduces a numerical analysis of noise-induced pattern transitions in delayed swarm systems, highlighting the role of noise thresholds and delay distributions.

Findings

Existence of a critical noise threshold for pattern transition

Transition time depends on noise intensity and delay distribution

Noise can induce more organized swarm states

Abstract

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the stability of a class of emerging patterns depends upon all moments of the time delay distribution, and predicts their bifurcation parameter ranges. Near the bifurcations of these patterns, noise may induce a transition from one type of pattern to another. We study the onset of these noise-induced swarm re-organizations by numerically simulating the system over a range of noise intensities and for various distributions of the delays. Interestingly, there is a critical noise threshold above which the system is forced to transition from a less organized state to a more organized one. We explore this phenomenon by quantifying this critical noise threshold, and note that transition time between states varies as a function of both the noise intensity and delay distribution.