Trail formation based on directed pheromone deposition

Emmanuel Boissard, Pierre Degond, Sebastien Motsch

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1267-1301
Number of pages35
JournalJournal Of Mathematical Biology
Issue number6
StatePublished - May 2013
Externally publishedYes


  • Alignment interaction
  • Directed pheromones
  • Fluid models
  • Individual-Based Model
  • Kinetic models
  • Pattern formation
  • Pheromone deposition
  • Self-propelled particles
  • Trail detection

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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