Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach

TL;DR

This paper introduces a multiscale method using an advection-diffusion equation with memory to analyze collective motion and decision-making in swarms, based on projecting particle configurations onto a meta-particle.

Contribution

The novel approach projects swarm configurations onto a meta-particle and derives an advection-diffusion equation with memory to predict collective behavior.

Findings

Accurately predicts transport properties of swarm configurations.

Provides a coarse-grained analysis from individual-based models.

Links particle dynamics to macroscopic collective states.

Abstract

We propose a (time) multiscale method for the coarse-grained analysis of self--propelled particle models of swarms comprising a mixture of `na\"{i}ve' and `informed' individuals, used to address questions related to collective motion and collective decision--making in animal groups. The method is based on projecting the particle configuration onto a single `meta-particle' that consists of the group elongation and the mean group velocity and position. The collective states of the configuration can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle. These properties can be accurately predicted by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model.