Statistical multi-moment bifurcations in random delay coupled swarms

TL;DR

This paper investigates how random discrete time delays influence the collective behavior of self-propelling particle systems, revealing that different pattern bifurcations depend on various moments of the delay distribution.

Contribution

It introduces a mean field approximation to analyze bifurcations, showing universal pattern characteristics linked to moments of the delay distribution, both theoretically and numerically.

Findings

Bifurcations of simple patterns depend only on the first moment of delay.

Complex pattern bifurcations depend on all moments of the delay distribution.

The study combines theoretical analysis with numerical simulations.

Abstract

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.