Trail formation refers to the phenomenon known in colonies of ants or herds of animals where the agents form robust trails or lanes along which they move collectively. This phenomenon originates in the delayed and long-range interaction between the agents caused by signalling chemicals or leaving footsteps.
We consider a minimal agent-based model of self-propelled particles and chemicals (e.g., a pheromone), both treated as discrete entities with agents depositing and sensing the chemicals and acting according to an alignment rule. Based on extensive computer simulations, we show that the model supports the spontaneous formation of a stable, macroscopic trail.
The non-equilibrium phase diagram of the model is spanned by the strength of the agent-pheromone interaction, and the number density of the population. Exploring this parameter space, we identify a number of distinct stationary phases.