Spontaneous trail formation in populations of auto-chemotactic walkers

TL;DR

This paper investigates how populations of self-propelled agents, inspired by insects like ants, spontaneously form persistent trails through pheromone-based interactions, revealing phase transitions and pattern formation via simulations.

Contribution

It introduces a detailed off-lattice simulation model for trail formation in auto-chemotactic agents and identifies phase transitions and macroscopic trail patterns.

Findings

Spontaneous formation of persistent, macroscopic trails.

Identification of a non-equilibrium state diagram.

Evidence of a dynamic phase transition with a potential order parameter.

Abstract

We study the formation of trails in populations of self-propelled agents that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g., ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium state diagram of the model, spanned by the strength of the agent--pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation.