WIAS Preprint No. 2900, (2021)

Spontaneous trail formation in populations of auto-chemotactic walkers


  • Mokhtari, Zahra
  • Patterson, Robert I. A.
    ORCID: 0000-0002-3583-2857
  • Höfling, Felix

2020 Mathematics Subject Classification

  • 92C05 82C22


  • Chemotaxis, trail, active matter, agent models, collective behaviour




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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