Trail formation based on directed pheromone deposition

TL;DR

This paper introduces an individual-based model for ant-trail formation using directed pheromones and alignment interactions, revealing a phase transition and comparing kinetic and fluid descriptions of trail development.

Contribution

It presents a novel self-propelled particle model with directed pheromones and analyzes phase transitions and fluid approximations for ant-trail formation.

Findings

Existence of a phase transition with increased ant-pheromone interaction frequency.

Fluid models require additional mechanisms for trail pattern development.

Kinetic and fluid descriptions provide complementary insights into trail formation.

Abstract

We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromones and interact with them through alignment interaction. The directed pheromones intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail when it meets it. Thanks to adequate quantitative descriptors of the trail patterns, the existence of a phase transition as the ant-pheromone interaction frequency is increased can be evidenced. Finally, we propose both kinetic and fluid descriptions of this model and analyze the capabilities of the fluid model to develop trail patterns. We observe that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level.