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Trail formation based on directed pheromone deposition

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Abstract

We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromone particles and interact with them through alignment interaction. The directed pheromone particles intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail when it meets it. Thanks to adequate quantitative descriptors of the trail patterns, the existence of a phase transition as the ant–pheromone interaction frequency is increased can be evidenced. We propose both kinetic and fluid descriptions of this model and analyze the capabilities of the fluid model to develop trail patterns. We observe that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, UPS, INSA, UT1, UTM, Université de Toulouse, 31062, Toulouse, France

    Emmanuel Boissard & Pierre Degond

  2. Institut de Mathématiques de Toulouse UMR 5219, CNRS, 31062, Toulouse, France

    Emmanuel Boissard & Pierre Degond

  3. Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742-4015, USA

    Sebastien Motsch

Authors
  1. Emmanuel Boissard
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  2. Pierre Degond
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  3. Sebastien Motsch
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Correspondence to Sebastien Motsch.

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Boissard, E., Degond, P. & Motsch, S. Trail formation based on directed pheromone deposition. J. Math. Biol. 66, 1267–1301 (2013). https://doi.org/10.1007/s00285-012-0529-6

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  • DOI: https://doi.org/10.1007/s00285-012-0529-6

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