Journal of Mathematical Biology

, Volume 66, Issue 6, pp 1267–1301 | Cite as

Trail formation based on directed pheromone deposition

  • Emmanuel Boissard
  • Pierre Degond
  • Sebastien MotschEmail author


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.


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

Mathematics Subject Classification

35Q80 35L60 82C22 82C31 82C70 82C80 92D50 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Emmanuel Boissard
    • 1
    • 2
  • Pierre Degond
    • 1
    • 2
  • Sebastien Motsch
    • 3
    Email author
  1. 1.Institut de Mathématiques de Toulouse, UPS, INSA, UT1, UTMUniversité de ToulouseToulouseFrance
  2. 2.Institut de Mathématiques de Toulouse UMR 5219, CNRSToulouseFrance
  3. 3.Center for Scientific Computation and Mathematical Modeling (CSCAMM)University of MarylandCollege ParkUSA

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