Cluster formation and anomalous fundamental diagram in an ant trail model

TL;DR

This paper analyzes a stochastic cellular automaton model of ant trails, revealing how pheromone evaporation influences ant flux and speed, leading to cluster formation and an unusual non-monotonic relationship between density and speed.

Contribution

It provides a detailed analysis of the ant trail model, explaining the formation of loose clusters and the non-monotonic speed-density relationship through phenomenological and microscopic approaches.

Findings

Ant flux is sensitive to pheromone evaporation probability.

Average ant speed varies non-monotonically with density.

Loose clusters form, affecting overall flow dynamics.

Abstract

A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35, L573 (2002)}), motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies non-monotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatio-temporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.