Journal of Mathematical Biology

, Volume 72, Issue 6, pp 1579–1606 | Cite as

A model for collective dynamics in ant raids

  • Shawn D. RyanEmail author


Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and the transition from one class of ants to another. Through analysis of an order parameter measuring the orientational order in the system, the model shows self-organization into a collective state consisting of lanes of ants moving in opposite directions as well as the transition back to the individual state once the food source is depleted matching prior experimental results. This indicates that in the absence of direct communication ants naturally form an efficient method for transporting food to the nest/bivouac. The model exhibits a continuous kinetic phase transition in the order parameter as a function of certain system parameters. The associated critical exponents are found, shedding light on the behavior of the system near the transition.


Collective motion Phase transition Coupled PDE/ODE model Ant raiding Social insect behavior Critical exponents 

Mathematics Subject Classification

34F05 35Q92 70B05 92B05 



Thank you to Paulo Amorim, Gil Ariel, and Magali Tournus for useful discussions. The author gratefully acknowledges support from National Science Foundation Grant DMS-1212046 and advice from X. Zheng (KSU) and P. Palffy-Muhoray (KSU). The work of SR was supported by National Science Foundation Grant DMS-1212046.

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematical Sciences and Liquid Crystal InstituteKent State UniversityKentUSA

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