A recently proposed stochastic cellular automaton model [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 nonmonotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatiotemporal 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.

• Received 29 November 2002

DOI:https://doi.org/10.1103/PhysRevE.67.036120