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arXiv · 2112.11907

Spontaneous trail formation in populations of auto-chemotactic walkers

Zahra Mokhtari·Robert I. A. Patterson·Felix Höfling
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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.

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Zahra Mokhtari, Robert I. A. Patterson, Felix Höfling. 2021-12-08. Spontaneous trail formation in populations of auto-chemotactic walkers. https://doi.org/10.1088/1367-2630/ac43ec

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